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Computational OT #3 - Dual and semidiscrete

Gabriel Peyré
April 09, 2025
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Computational OT #3 - Dual and semidiscrete

A course on computational optimal transport

Gabriel Peyré

April 09, 2025
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  1. Dual and Semi-discrete Numerical Optimal Transport Gabriel Peyré É C

    O L E N O R M A L E S U P É R I E U R E www.numerical-tours.com http://optimaltransport.github.io
  2. Discrete Dual Problem Wc(a, b) = min P2Rn⇥m + hC,

    Pi : P1 = a, P>1 = b <latexit 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  3. Discrete Dual Problem = min P2Rn⇥m + max f2Rn,g2Rm hC,

    Pi + hf, a P1i + hg, b P>1i <latexit 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<latexit 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<latexit 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Wc(a, b) = min P2Rn⇥m + hC, Pi : P1 = a, P>1 = b <latexit 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<latexit 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  4. Discrete Dual Problem = max f2Rn,g2Rm hf, ai + hg,

    bi + min P2Rn⇥m + hC, Pi hf, P1i hg, P>1i <latexit 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<latexit 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<latexit sha1_base64="xD9q06rTZjW94zgCM8TF494RYlA=">AABF4XictVzddhu3EYbSv1jpj9Ne9fRmE8U9TqK4kuue9jQnp7ElWVKs2LRJyU5MS4dLLum1l1yaS8o/DB+gdz297WP0AfocfYP2qq/QwQywwJLYHazqeo8kLBbfzGAWGMwMsA7HSZxNt7b+ufbO977/gx/+6N1L6+/9+Cc//dnl939+kqWzSTc67qZJOnkUdrIoiUfR8TSeJtGj8STqDMMkehg+35HPH55HkyxOR63p63H0ZNgZjOJ+3O1Moers8t+/CNofyGu9PRt2Xs3b/aAdj4L2gweno832IL8ZLgJq1UunY2i1mLc7i/VPA3U/gPsQ7xWpeDRvNzT67NPTORSm8TDKguFiEWgyOwBrLNY/CyyygEpHUWbVSuKN0/Y0HdOTs8sbW9e28F+wWthWhQ2h/jXS9z98T7RFT6SiK2ZiKCIxElMoJ6IjMrgei22xJcZQ90TMoW4CpRifR2Ih1gE7g1YRtOhA7XP4PYC7x6p2BPeSZoboLnBJ4GcCyEBcAUwK7SZQltwCfD5DyrK2jPYcaUrZXsPfUNEaQu1UPIVaDqdb+uJkX6aiL/6AfYihT2Oskb3rKioz1IqUPLB6NQUKY6iT5R48n0C5i0it5wAxGfZd6raDz/+FLWWtvO+qtjPxb5TyClyBaKrepzmFjjhH+gG+zRk8I3kS4DwACpHqoyy9RF0PsfcjaD+H+rtwLbCkdRLCNcfaRSVyBy4XcodF7sPlQu6zyCO4XMgjFtmAy4VsKKTETlDnbnwTLhe+yXK+D5cLeZ9FPoDLhXzAIk/gciFPWOS3cLmQ37LI23C5kLdZ5B24XMg7LLIFlwvZYpHHcLmQxyxyDy4Xck8hy2fqBK4U6cTMrLwJ5SIPaSkSqLnJyncLraMLe8tjTndLsPys3oW/buyuh06jEuyex7jrl2D5kbcPNtKN5W3RAa4mLuwBiz2EEeDGHrLYr8SzEuxXHjPteQmWn2tH0M6N5a3v13Dnxn7NYu9CyY3l16h7UOPG3vNYMcYl2AaLvS9elGB9rP6kBMvb/SbYFTeWX6da0N6N9bGmsxIsb09PwINxY/nV6iHUurEPWewj8aoE+4jFfgPW3Y39xmOFfVOC1WvsOq4gA/RHIpixVdQ6+ayUpTFQ6zD8k3xtSdA3DqGewwxyzAAxQxaxnyP2PRFHOeLIW64st6MZ+rs8l2aOaHoiwnxtkqUp276Xt5elxAOxmyN2lxBVHql817ov5+hd6BoOOc1XLlny6VOa229ZitR4qLa8GnGvgKCx/RRH/iZGSzKCkpqqovY0X+MJGeB9FeIlRm+6l5oHj5vmVsFGvWJRoQMVsqjXDtRrFjVzoGYs6tyBOmdRZubbuLbHCDD6l+9ijnc0AshHLr8C8ApuwqpzAHM0gPHTAC/wAdbcg79NjL25q0oyGc3LdVJmOZ4ULPEESnOxAfUmKtzF+DrBGRaBZNTynorx5Z3MbczVnCMrvMhX8iDPmPjTiVGeQU5HeosBzqd6dO5gzQK9OyrVwx/k816X6uH3UOML9OKpVA8/VdJPLyB7S2FbF8A2YTaNlfZNuS4Nyr8QDV1ex1VXWlz5VodqzEh6r2rSP1Rv5vAC72UHS6QfU65HI7P6lxX6V4eG0XNm6bkeFek9kderS0HtnoxU3GvKdWVIcRUdKTnMXd03I9v01JvR5Xo0GuBx7WDMPbfKdUfvOO+NKdejcSIo77lAT16X69EY4D3pw5Tr0ZDZlo6K8025rmWXGqDY2ZTrWvURZoFlDojGPNUYr2iCftJMUYvRP6jO1tg+/+o6JnM2p3mMUE3J+LbldMJ8LauWSPsLEVi1aU05pH8xs3ywIo25uM7GVyTDtLC+r9Ixa7zU/BFoMYDZT3sAXM48AQl1TkJa7wQobrNRV7FnGnedxclR0l9CtVXtlPUWDV/KGhXrzrCWi8tMb40e22ivMxx7Y/QJj1CznB6OSt9wGUVOQ0cFDfH06ujujZqvRe1vsbjxEmKcj7Qu7gjRTlp1nOrSetPS8RW1yzOFi/Z8zPiV2ea+sjYy5knRFklZqnja7XQeya6T6+qmMDluehbgG5X26hytRow7UhkbhepsMXnjc7w3tI9xT07yIBpdeI+BojIWtGsms+gynx6gRbXtLcdb6ktn6KicodXV9rgaPbDQAwe6foyzAyvGXSi1IGY4hruWR5SznusqRY1PxGf57miKb7A6ok8KFlLTIHsTFSxkVZT9tEDlJaDlaKAo3Z/GMh2Nb69Q4qN+lzwmdi1a/iu4c6v3tzs4xstHc3kmpodcryPXAGcN7erS3TIHkmDufHId/dfqXkp+dThKG8pxPbU4k15GuOMfYQQ7Rs84wdnGzY5iazs/tfxEc2oIvXcud7NTtJAB2r8A1qcUx2SAP/bZAb2DThYhQRvpY3fi3Ltx+ToxO8aMHxcLOtVgxluEtmyG/DVde3ZlOBYpYqB1YLE0trVOjtAXjJDrRFl3M7erVx+JNOck7FFCFM1YuYr8P8bf+kePk42VESE1LN9Apmyd632kGLNIHXVwla+2QbqtLeVHuQynSmqz/hmZPipItosRl5RHrtY94NzFe+IlR8kE5c5W2tA6WpXNlZTHS3qUve1jFE92f6BWYCn3Jq6SGzjn2jhKBjAKpnkUodtyWeRlvtW8itT9aGf/F+pG10WtSYqBMBlc0hCX348wWrOlTGBU0/h9jrPJrfXJUqtqPiMci0NrLn8HtR/Aby23vvejExaswi0cA0TB3BmNUE2w0sKP160CLz0yNS1zb/iZMalb2TUXia/JupkY+7w2lQaOmlcqa6HLF6HxzKLxzFOHLdxrNFrU9doSnbGxRUvtVvryq8OtVYPyjKXMe2QaFXtIacdSflR7LFU+xteoNyytLZZWB2arvRtgz3kfpHuuL8/u7/LVPRC30bfpogdG8UsPZ2mMPpeurY7UiILkfEPZV3v2t7FGcg/RgkrKdI5Tzhjaderitcgl/bVa2VK088Yi6HNLL1UbbWPbWP7tCnKIcyLDeakRN7BFpOS35QiWLNI1y+cIMPPfQZ+K/I7qmNlubd5JUPAnTLxJs8rwokhhhPrnMm+HK9HroRW/BhgTzpR3HQKt+m9YUiCMziS4PcsM35Bc5WgngTzaEO3nqp2iXbyRJdE1lHouvvCwMRT1mrFujy3dY923T6Cl1Lp5664WPL/EmyPH7yI7eh1c1YbKR50v3V+MVketcsX7Kj3MlvgafcywjR1ZmCiviGmLz725kET1uBDGh0u9XtSRv57kdWSm3Slfyrq1plzMNJCNeYrxEncOVCJc3t1Vpzf3MdOPcIVeiFibGtVwlGQ2LlX5AdvSyqzUpZV1iGovVa5GibUSla0Umrq9Whj7TRYyQuuXCC5nQ61t2duFKIXPwhCFrqATvWXxoU3zc/FH/B0IV3SoOfrkDpvg394UO2LvLZyGeKHKlNEMsEbagt5S7N1R/Sy2qNbRC4u6Td+Hgz+PGHTNSR/jSlpXdqLMS25T96f/Eq3ARESs9KZl/T7YXPierHKq058YLRvfm1job3Hq9kVz8OlJkYs/H9rX4HrRF/qbpnp90NT5HhQ51OGhzzH4vXPTuj4vm1O1vla5+PKgVUDvuGic3Pkrj1VMOx8LNbHeyNvnIK1Dv4K6Xi3+135oPoZTfV6+3DL81uyZx1undpHKyEp/uP6cMdx8RnM5R3+ead474y25+ZHfF9R6U6nVm7dPX/qjZgxoXnNBeVBeOsLbo8jI60tF7gu4ZEjFf8Q/1vivEV7kNMrkqENJ71OUU9MteGr6i0tX7/QzH5kMnTKZitRMHNHEE7E74lDchp+d3AOsezqUvqWkvxLr/n62B7V9tB46i06ZgzbWRZj9MLtoPbw352fLJJZneelsbwtq5F74EdbKc753sb0869sq9K38CxKa61+LVPQKEcny7p6ZVyH0oLjzRjkg/Z1vgGfpKYtFJ8+GHnuLdH6KIiT91fMcET2MB5clnSNCj5YqyqGTcohnkaIS2qHVt+psYl2p+4LPFg0uIPGg8Da6OCfH6kyC3CGRXxJ08jxYIH6DdR21nknfgtNjwyHVY8xhhDhitiCm/J3YhL+bquyWtLEiaYajpijRK+tZ9Zm1hXMkm+8ur2DGTucUz1W7FPMPZp+z+i3vlnKh91mNH1TgB5aUTXxbzzFDMBHVWc5ZBc2ZksneeR4JnaElPcj4u5OPj+qI/7yC17lH/++Uou9Yku6DLCHuCwS48zhBeonSzR5KTydAqzPMBxXS6u9LiaY5A2rGgT7NWb17kahxVz7z6cQml1WKSujYc53OjnL7Kbw8vDQ+snBUZqwkM4+vms89ZDn3oNNnpOmzFAasJGoGn13e2F7+f0NWCyfXr21vXdu+f2Pjy1vq/xR5V/xKfCiuwnr6e/EljNCGOBbdtV+u/WntYO1wr7v3572/7P2Vmr6zpjC/EIV/e3/7L5YJjhY=</latexit> = min P2Rn⇥m + max f2Rn,g2Rm hC, Pi + hf, a P1i + hg, b P>1i <latexit 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<latexit 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<latexit 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Wc(a, b) = min P2Rn⇥m + hC, Pi : P1 = a, P>1 = b <latexit 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<latexit 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  5. Discrete Dual Problem = max f2Rn,g2Rm hf, ai + hg,

    bi + min P2Rn⇥m + hC, Pi hf, P1i hg, P>1i <latexit 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<latexit 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<latexit sha1_base64="xD9q06rTZjW94zgCM8TF494RYlA=">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</latexit> = min P2Rn⇥m + max f2Rn,g2Rm hC, Pi + hf, a P1i + hg, b P>1i <latexit 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<latexit 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<latexit 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Wc(a, b) = min P2Rn⇥m + hC, Pi : P1 = a, P>1 = b <latexit 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<latexit 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sha1_base64="k31DWOUFIeDNkCyXKSkoKxf19Uc=">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</latexit> = max f2Rn,g2Rm hf, ai + hg, bi + min P>0 hC (f1> + 1g>), Pi <latexit 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<latexit 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<latexit 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  6. Discrete Dual Problem = max f2Rn,g2Rm hf, ai + hg,

    bi + min P2Rn⇥m + hC, Pi hf, P1i hg, P>1i <latexit 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<latexit 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<latexit sha1_base64="xD9q06rTZjW94zgCM8TF494RYlA=">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</latexit> = min P2Rn⇥m + max f2Rn,g2Rm hC, Pi + hf, a P1i + hg, b P>1i <latexit 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<latexit 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<latexit 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Wc(a, b) = min P2Rn⇥m + hC, Pi : P1 = a, P>1 = b <latexit 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<latexit 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Wc(a, b) = max f2Rn,g2Rm {hf, ai + hg, bi : f g 6 C} <latexit 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<latexit 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<latexit sha1_base64="Fp8/Bm1WtGlj/5Jnfy4FKEwyHbE=">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</latexit> Theorem: <latexit 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<latexit 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<latexit sha1_base64="TfxVz7U9ZiSc7OyPcRoyjTWz4r8=">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</latexit> = max f2Rn,g2Rm hf, ai + hg, bi + min P>0 hC (f1> + 1g>), Pi <latexit 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<latexit 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<latexit sha1_base64="11/iPaErBp8ZuhBE64qxpX1gyqM=">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</latexit> min P>0 hQ, Pi = ⇢ 0 if Q > 0, 1 otherwise. <latexit 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<latexit 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<latexit 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  7. Discrete Dual Problem {(i, j) : Pi,j 6= 0} ⇢

    {(i, j) : fi + gj = Ci,j } <latexit 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<latexit 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<latexit 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Primal-dual relations: <latexit 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<latexit 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sha1_base64="mXT9YhX8L7lf5BdFBO1oNpSQe30=">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</latexit> = max f2Rn,g2Rm hf, ai + hg, bi + min P2Rn⇥m + hC, Pi hf, P1i hg, P>1i <latexit 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<latexit 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<latexit sha1_base64="xD9q06rTZjW94zgCM8TF494RYlA=">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</latexit> = min P2Rn⇥m + max f2Rn,g2Rm hC, Pi + hf, a P1i + hg, b P>1i <latexit 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<latexit 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<latexit 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Wc(a, b) = min P2Rn⇥m + hC, Pi : P1 = a, P>1 = b <latexit 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<latexit 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Wc(a, b) = max f2Rn,g2Rm {hf, ai + hg, bi : f g 6 C} <latexit 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<latexit 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<latexit sha1_base64="Fp8/Bm1WtGlj/5Jnfy4FKEwyHbE=">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</latexit> Theorem: <latexit 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<latexit 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<latexit sha1_base64="TfxVz7U9ZiSc7OyPcRoyjTWz4r8=">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</latexit> = max f2Rn,g2Rm hf, ai + hg, bi + min P>0 hC (f1> + 1g>), Pi <latexit 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<latexit 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<latexit sha1_base64="11/iPaErBp8ZuhBE64qxpX1gyqM=">AABFunictVzvchPJER9f/h2+/OGSL6nKlwUfKcj5iE1IJZXLVR3YxvgwIJBsuGOB0korIbzSCq1kDDq9Qd4pz5E3SD6lKk+Q7p6ZnVlpdnvWIWzZnh3Nr7unZ6anu2dENE4G2XRr6x9rH/3ghz/68U8+vrD+yU9/9vNfXPz0l8dZOpt04qNOmqSTp1E7i5PBKD6aDqZJ/HQ8idvDKImfRCc7+PmT03iSDdJRa/puHD8ftvujQW/QaU+h6uXFv30VhJfwWQ9nw/bZPOwF4WAUhI8fvxhthv38ZbgIZKtuOh1Dq8U8bC/WPw/Uex/eI3xHMoPRPGwEYT9+E2wtAg3Z+eJq2AvTUZy9CKfp+HMqhn16uQbwxmL95cWNretb9C9YLWyrwoZQ/xrpp5c/EaHoilR0xEwMRSxGYgrlRLRFBs8zsS22xBjqnos51E2gNKDPY7EQ64CdQasYWrSh9gR+9+HtmaodwTvSzAjdAS4J/EwAGYgrgEmh3QTKyC2gz2dEGWvLaM+JJsr2Dv5GitYQaqfiFdRyON3SF4d9mYqe+DP1YQB9GlMN9q6jqMxIKyh5YPVqChTGUIflLnw+gXKHkFrPAWEy6jvqtk2f/5NaYi2+d1TbmfgXSXkFnkA0Ve/TnEJbnBL9gEZzBp9JeRLg3AcKseojlt6SrofU+xG0n0P9A3gWVNI6ieCZU+2iErkDjwu5wyL34XEh91nkITwu5CGLbMDjQjYUErET0rkb34THhW+ynB/B40I+YpGP4XEhH7PIY3hcyGMW+R08LuR3LPIOPC7kHRZ5Dx4X8h6LbMHjQrZY5BE8LuQRi9yDx4XcU8jylTqBJyU6A2ZV3oJykQdaigRqbrHy3Sbr6MLe9ljTnRIsv6p34a8bu+uh07gEu+cx73olWH7m7YONdGN5W3SXdhMX9i6LPYAZ4MYesNhvxOsS7DceK+2kBMuvtUNo58by1vc+vLmx91nsAyi5sfwe9RBq3NiHHjvGuATbYLGPxJsSrI/Vn5RgebvfBLvixvL7VAvau7E+1nRWguXt6TF4MG4sv1s9gVo39gmLfSrOSrBPWey3YN3d2G89dtj3JVi9x67TDtInfySGFVtFrZ2vSiyNgVqb4Z/ke0tCvnEE9Rymn2P6hBmyiP0cse+JOMwRh95yZbkdzcjf5bk0c0TTExHlexOWpmz7bt4eS4kHYjdH7C4hqjxSHGvdl1PyLnQNh5zmOxeWfPqU5vYbS7GaD9WWVyMeFhBybr+imb9J0RJGUKipKmqv8j1eIgN6r0K8pehN91Lz4HHT3CrYqDMWFTlQEYt650C9Y1EzB2rGok4dqFMWZVa+jQs9ZoDRP47FnN7kDJA+cvkTgFdwC3adu7BGA5g/DfACH1PNQ/jbpNibe6okw2ge90nMcjwvWOIJlOZiA+pNVLhL8XVCKywGyWTLhyrGxzfMbczVmpNWeJHv5EGeMfGnMyB5+jkd9BYDWk/16NyjmgV5d7JUD383X/e6VA+/RxpfkBcvS/XwUyX99ByytxS2dQ5sE1bTWGnflOvSkPkXSUOX12nXRYuLozpUcwbpndWkf6BG5uAc47JDJakfU65HI7P6lxX6V4eG0XNm6bkeFfSepNerS0HtnoxU3GvKdWVIaRcdKTnMW92RwTZdNTK6XI9GAzyuHYq551a57uwd570x5Xo0joXMey7Ik9flejT69C71Ycr1aGC2pa3ifFOua9lRAzJ2NuW6Vn1EWWDMAck5L2uMVzQhP2mmqA3IP6jO1tg+/+o+hjmbF3mMUE3J+LbldKJ8L6uWSPsLMVi1aU050L+YWT5YkcZc3GDjKynDtLC/r9Ixezxq/hC0GMDql2cAXM48AQl1TgKtdwIUt9moq9gzjbvB4nCW9JZQoaqdst6i4SuzRsW6l1TLxWWmt0aPIdnrjObemHzCQ9Isp4fD0hEuo8hp6LCgIZ5eHd29V+u1qP0tFjdeQozzmdahEyF5klYdp7q03rR0fEWd8kzhkWc+Zv5itrmnrA3GPCnZIpSliqfdTueR7DrcVzeFyXHLzwIaUbRXp2Q1BnQilbFRqM4WS298Tu+G9hGdySEPSaMD4xgoKmMhT80wi4759IAsqm1vOd6oL52hk+WMrK62x9XovoXuO9D1Y5wd2DEeQKkFMcMRvLU8opz1XFcpaXwivshPR1MaweqIPilYSE1D2pu4YCGrouxXBSpvAY2zQUbp/jSW6Wh8uEKJj/pd8pjYtWj5r9DJrT7fbtMcL5/N5ZmYLnG9QVwDWjXyVFe+LXOQEsydn9wg/7W6l8ivDke0oRzXFxZnqZcRnfjHFMGOyTNOaLVxq6PY2s5PLX+iOTWEPjvH0+yULGRA9i+A/SmlORnQj313QJ+gS4uQkI30sTuD3Ltx+ToDdo4ZP24g5K0GM99ismUz4q/p2qsro7koIwa5DyyW5rbWySH5gjFxnSjrbtZ29e6DSHNPwp4lkqKZK1eJ/zX6rX/0PNlYmRGoYRyBTNk613ikFLOgjtq0y1fbIN3WlvKzXIYXSmqz/xmZPitItksRF8qDu3UXOHfoXfLCWTIhubOVNnIfrcrmIuXxkh6xtz2K4qXd76sdGOXepF1yg9ZcSLOkD7NgmkcRui2XRV7mW82rSN2PdvZ/oW50XdQaUgyEyeBKDXH5/ZiiNVvKBGa1nL8ntJrcWp8starmM6K5OLTW8vdQewl+a7n1ux+dqGAVbtMckBTMm9GIrAlWWvjxul3gpWempmXeDT8zJ3Uru+Y88bW0bibGPq1NpUGz5kxlLXT5PDReWzRee+qwRWeNRou6Xluil2xs0VKnlb786nBr1aA8YynzHplGDTyktGMpP6pdliof42vUe5bWFkurDavVPg2w17wP0r3Wl1f39/nuHog75Nt0yAOT8UuXVumAfC5dWx2pSQrI+aayr/bqD6kGuUdkQZGyvMeJK0aeOnXoWeSS/lbtbCnZeWMR9L2lt6qNtrEhlf+wghzSmshoXWrETWoRK/ltOYIli3Td8jkCyvy3yaeSfkd1zGy3NmMSFPwJE2/KVWV4yUhhRPrnMm8HK9HrgRW/BhQTzpR3HQGt+iOMFCRGZxLcnmVGI4S7nDxJkB5tRPZz1U7JU7yRJdF1knouvvKwMTLqNXPdnlu6x7pvv4OWqHUz6q4WPL/EmyPH7zwnem3a1YbKR50vvZ+PVlvtcsX3Kj3MlvgafcyojR1ZmCiviAnFl95cpET1uEiMD5d6vagjfz3J68gsT6d8KevWmnIx0yBtzCuKl7h7oIhweXdXnd7cNaYf0Qq9iLA2NVnDUcJsXKryA7alxazUhZV9SNZeqNyNEmsnKtspNHV7tzD2W1rImKxfIricjWxtyx4WohQ+CyMpdIS80VsWH9o0vxR/od+BcEWHmqNP7rAJ/u0tsSP2PsBtiDeqLDOaAdWgLeguxd5t1c9ii2odvbGo2/R9OPjzGICuOekHtJPWlV1S5iW3qfvTf0tWYCJiVnrTsn4fbC58T1Y51enPgCwb35uB0N/FqdsXzcGnJ0Uu/nzkuQbXi57Q32mq1wdNne9BkUMdHvoeg9+Ym9b1edmcqvW1ysWXh9wF9ImLxuHJX3msYtr5WKiJNSIfngNah14Fdb1b/K/90HwMp/q8fLll9F2z1x6jLtvFKiOL/nD9NWO4+czmco7+PNO8d8ZbcvOTfl9Qa6RSqzcfnj76o2YOaF5zIfOgvHQSb88iI68vFTwXcMmQin+Lv6/x30Z4k9Mok6MOJX1OUU5Nt+Cp6W9cunqnP/ORydApk6lIzcQRTboRuyMOxB342ck9wLq3Q+V3KeVfxLq/P9uF2h5ZD51Fl5mDkOpiyn6YU7QuvZv7s2US411eebe3BTV4Fn5ItXjP9wG1x7u+rULfyr9BItf6fZGKbiEiWT7dM+sqgh4UT95kDkh/zzegu/QyiyVvng09zhbl/SkZIelvPc8J0aV4cFnSOSH0bKmiHDkpR3QXKS6hHVl9q84m1pW6J/hsUf8cEvcLo9GhNTlWdxLwhAS/SdDO82CB+D3VtdV+hr4Fp8eGQ6pnlMOIaMZsQUz5R7EJfzdV2S1pY0XSjGZNUaIz67PqO2sL50w237u8Qhk7nVM8Ve1Syj+Yc87qUd4t5SLHsxrfr8D3LSmbNFonlCGYiOos56yC5kzJZJ88j4TO0Eo9YPzdzudHdcR/WsHr1KP/90rR9yxJ90GWiM4FAjp5nBC9ROlmj6SXN0CrM8x3K6TV3y+VNM0dUDMP9G3O6tOLRM278pUvb2xyWaW4hI691uXdUe48hZeHl8ZHFo7KjJVk5vGt5lMPWU496PQYaXoshT4riVrBLy9ubC//vyGrheMb17e3rm8/urnx9W31f4p8LH4jLoursJ/+SXwNM7QhjoDTf9Z+vXZp7fLeX/eivcHeiWz60ZrC/EoU/u1N/wu6Wn9G</latexit> min P>0 hQ, Pi = ⇢ 0 if Q > 0, 1 otherwise. <latexit 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<latexit 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<latexit 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  8. Continuous Dual Problem hf, ↵i def. = Z X f(x)d↵(x)

    <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="se5IX5+6njWKy85BP15PzazVNiY=">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</latexit> ↵ = P i ai xi <latexit 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<latexit 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sha1_base64="he7kQ98qCVO2MLGOmG/ISS/zGmM=">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</latexit> f = (f(xi))i <latexit 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<latexit 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<latexit sha1_base64="FXXrDSJSbBUCdTCgZ7J0/L8mavc=">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</latexit> hf, ai def. = P i fiai <latexit 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<latexit 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Wc(↵, ) = min ⇡2M+(X⇥Y) {hc, ⇡i : ⇡1 = ↵, ⇡2 = } <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  9. Continuous Dual Problem hf, ↵i def. = Z X f(x)d↵(x)

    <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="se5IX5+6njWKy85BP15PzazVNiY=">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</latexit> ↵ = P i ai xi <latexit 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<latexit 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sha1_base64="he7kQ98qCVO2MLGOmG/ISS/zGmM=">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</latexit> f = (f(xi))i <latexit 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<latexit 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<latexit sha1_base64="FXXrDSJSbBUCdTCgZ7J0/L8mavc=">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</latexit> hf, ai def. = P i fiai <latexit 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<latexit 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<latexit sha1_base64="JiXKd22Cbax9asEhjpJf4ehSfA0=">AABGCnictVzbchu5EYU3t7Vy8yaPeZms7NRuynEkZVNJZStVa0uyrDVtyyYle23aKl6G9Ngkh+ZFvnD5B/mavKXykDzkJ/IDqeQp+YT0BRhgSMw0RnE8JQmDwelu9ACN7gbG7fEgmc62tv5+4YNvfPNb3/7Ohxc3vvu97//gh5c++tHJNJ1POvFxJx2kk0ft1jQeJKP4eJbMBvGj8SRuDduD+GH75S4+f3gWT6ZJOmrM3o7jp8NWf5T0kk5rBlWnlx5fbnbT2XgRLZpEbDGJu8uoeRJ3ZnfSbrzoLZfRctFsQV38qhv3ouZ0PjxNoo3C9qcJ3LdOk8unlza3rm3Rv2i9sK0Lm0r/O0o/+rimmqqrUtVRczVUsRqpGZQHqqWmcD1R22pLjaHuqVpA3QRKCT2P1VJtAHYOrWJo0YLal/C7D3dPdO0I7pHmlNAd4DKAnwkgI3UFMCm0m0AZuUX0fE6UsbaI9oJoomxv4W9b0xpC7Uw9h1oJZ1qG4rAvM9VTv6U+JNCnMdVg7zqaypy0gpJHTq9mQGEMdVjuwvMJlDuENHqOCDOlvqNuW/T8n9QSa/G+o9vO1b9IyitwRaque59mFFrqjOhH9Dbn8IzlGQDnPlCIdR+x9Jp0PaTej6D9AurvwrWkktFJG64F1S5Lkbtw+ZC7IvIALh/yQETW4PIhayLyCC4f8kgjETshnfvxdbh8+LrI+T5cPuR9EfkALh/ygYg8gcuHPBGRj+HyIR+LyJtw+ZA3ReRtuHzI2yKyAZcP2RCRx3D5kMcich8uH3JfI4tn6gSulOgkwqy8DuU8D7QUA6i5Lsp3g6yjD3sjYE53CrDyrN6Dv37sXoBO4wLsfsC46xVg5ZF3ADbSj5Vt0S1aTXzYWyL2EEaAH3soYr9ULwqwXwbMtJcFWHmu1aCdHytb3ztw58feEbF3oeTHymvUPajxY+8FrBjjAuyRiL2vXhVgQ6z+pAAr2/062BU/Vl6nGtDejw2xpvMCrGxPT8CD8WPl1eoh1PqxD0XsI/WGsFi2PuqCvAC0ZOs0HxHNcqpfgd33UUW/bE5Wbp3uVwF0H6t3BT01K/MGrTt9kj+GeV5GrZXNZSyNgVpL4D/IVqQBedRtqJcw/QzTJ8xQRBxkiINARC1D1ILlmmbWd0pessylniHqgYh2tqJhaSa272btsTQIQOxliL0VRJkfi+/a9OWMfBJTIyFn2XqHpZA+pZnVx1Ksx0O5vTaIezkEj+3nNPKvUoyFcRdqqoza88wzYGRE92WI1xTzmV4aHjJupm1JHvVGRLU9qLaIeutBvRVRcw9qLqLOPKgzEWVnvotrBowAq398Fwu64xHAnnXxFYEvcR3WqlswRyMYP0fgOz6gmnvwt04Ru3SVSYY5AFxdMTfyNGeJJ1BaqE2ot7HkHkXlA5phMUjGLe/pzADe8brAc46t8DJb/6MszxJOJyF5+hkd9DEjmk/V6NymmiX5hFyqhr+VzXtTqobfJ40vyffnUjX8TEs/O4fsDY1tnANbh9k01tq35ao0OGvDNEx5g1ZdtLj4Vod6zCC9NxXpH+o3c3iO97JLJdaPLVejMXX6N831rwoNq+epo+dqVNB7Yl/ZlKLKPRnpaNmWq8qQ0io60nLYu6pvBtt09Zsx5Wo0jsDj2qVIfeGUq47ecdYbW65G40RxtnRJ/r8pV6PRp3vWhy1Xo4E5mpbODthyVcuOGuCI25arWvUR5Y4xc8RjnmusVzQhP2muqSXkH5TneFyff30dw0zPsyxGKKdkfdtiOu1sLSuXyPgLMVi1WUU50L+YOz5YnsZC7YjxFcswy63v63TsGo+ar4EWI5j9vHMgZdox/jOZDLTeA6C4LUZd+Z4Z3I6Iw1HSW0E1de1M9BYtX8415etOqVaKy2xvrR6bZK+nNPbG5BPWSLOSHmqFb7iIoqShWk5DMr0qunun52te+1sibryCGGcjrUP7SLz/Vh6n+rRed3R8Re8NzeDinSI7fjFH3dPWBmOelGwRylLG021nsk9uHa6rV5XNjPOziN4o2qszshoJ7WNNxSjU5JjZG1/QvaV9TDt5yINpdOA9RprKWPFeG+beMQsfkUV17a3EG/Vl8npcnpLVNfa4HN130H0PunqMswsrxl0oNSBmOIa7RkCUs5HpKiWNT9Qvsj3VlN5geUQ/yFlIQ4PtTZyzkGVR9vMcldeAxtHAUXo4jVU6Bt9coyRH/T55bOyat/xXaL/X7Iq3aIwXj+biTEyXuO4Q14hmDe8F890qB5Zg4X2yQ/5reS+RXxWOaEMlrs8czqyXEZ0TiCmCHZNnPKDZJs2OfGs3P7X6xHA6UmbHHffAU7KQEdm/CNanlMZkRD/uiQOz784WYUA2MsTuJJl34/N1EnGMWT8uUXwWwo63mGzZnPgbuu7smtJY5IiB14Hlytg2OqmRLxgT14m27nZul68+iLSnK9xRwhTtWPmE+H9Kv82PGSebayMCNYxvYKptne99pBSzoI5atMqX2yDT1pXycibDMy21Xf+sTJdzku1RxIXy4GrdBc4dumdeOEomJPd0rQ2vo2XZXKQ8XtEj9rZHUTzb/b5egVHuq7RKbtKca9Io6cMomGVRhGkrZZFX+ZbzylMPoz39v1C3us5rDSlGymZwWUNSfj+maM2VcgCjmsfvS5pNfq1PVlqV8xnRWBw6c/lrqP0p/DZym/swOu2cVbhBY4Ap2DurEa6J1lqE8bqR42VGpqFl7y0/OyZNK7fmPPE1WzcbY59VpnJEo+aNzlqY8nlovHBovAjUYYN2KK0WTb2xRKdibNHQe5yh/Kpwa1SgPBcpyx6ZQSUBUrqxVBjVrkhVjvEN6p1Ia0uk1YLZ6u4GuHM+BOmf66uz++tsdY/UTfJtOuSBcfzSpVmakM9lassjNaaAnD/T9tWd/U2qQe5tsqBImU9/4ozhXacOXctM0p/plS0lO28tgjnt9Fq3MTa2SeVfrSGHNCemNC8N4jNqEWv5XTmiFYt0zfE5Isr8t8inYr+jPGZ2W9t3EuX8CRtv8qyyvDhSGJH+pczb4Vr0eujErxHFhHPtXbeBVvU3jBQYYzIJfs9ySm8IVzneSWCPtk32c91O8S7eyJHoGkm9UL8PsDEc9dqx7o4t02PTt59DS9S6feu+FjK/QTBHid95dvRatKoNtY+6WLk/H62WXuXy92V6mK/wtfqYUxs3srBRXh7TVJ8Hc2GJqnFhTAiXar2oIn81yavIzLtToZRNa0M5n2lgG/Oc4iXp9CgifN7dJ15v7lOhH+01em3CutS4RqKE2bhU5wdcS4tZqYtr6xDXXixdjQbOSlS0Uhjq7mph7TdbyJis30BJORtu7crezEUpchaGKXQUnwMuig9dmp+r39HvSPmiQ8MxJHdYB//2utpV++/hNMQrXeaMZkQ1aAu6K7F3S/cz36JcR68c6i79EA7hPBLQtSR9QitpVdmZsiy5Sz2c/muyAhMVi9LbltX74HKRe7LOqUp/ErJscm8SZb7gqdoXwyGkJ3ku4Xx4X0PqRU+ZL6Gq9cFQl3uQ51CFhznHEPbObevqvFxO5fpa5xLKg1cBs+NicLjzVxyr2HYhFmrivJH3zwGtQ6+Eulkt/td+GD6WU3Veodym9IXai4C3zu1inZFFf7j6nLHcQkZzMcdwnmnWO+st+fmx3xdVelOp05v3Tx/9UTsGDK+F4jyoLB3j3VFk5Q2lgvsCPhlS9W/1lwvyNwyvMhpFclShZPYpiqmZFjI1852mr3fmWYhMlk6RTHlqNo6o04nYXXWobsLPbuYBVj0dyl9g8l/E+r+67UJtj6yHyaJz5qBJdTFlP+wuWpfu7fnZIonxLC+f7W1ADe6F16gWz/nepfZ41reR61vxdyc81++oVHVzEcnq7p6dV23oQX7njXNA5uvgiM7ScxaLT54NA/YW+fwUR0i+71BWJV0QwoyWMsptL2X3W5R12u1c3zo0wsd6hx/3G/BcfivLKkXql1TX0qsDrtSSVEceqZ5QRqBN+t+CCO3X6ir8varLfkmPlJx9GoNMu+fiN852dY0epvSG8/194zwrP1+29I46+2XlFcqumfzfmW6XUq7A7kmW53f3CrnwOfpyfL8E33ekrNNYeEnR/ESVZyTnJTTnWiZ3l3ikTDaV9YCxcisbfeXR+VkJr7OA/t8uRN92JD0AWdqUw49ol3BC9AZaN/skPZ/WLM8G3yqR1nxByjTteU07DszJy/KdhoF37Lu2hU9XShmguICOa0n4nKdsk8xZz3KZzPnUEBsXB8k2c+gVyybrS9ZWiK4kKnNRknnAd9VnAbKcBdDpCdL0RAp9URJtYU4vbW6v/s8l64WTnWvbW9e27+9sfnFD/68mH6qfqI/VJ7A2/0Z9ATPoSB0Dp7+qf4DH95/9P+z/cf9P+3/mph9c0Jgfq9y//b/9FzOmj4Y=</latexit> max f2C(X),g2C(Y) ⇢Z X f(x)d↵(x) + Z Y g(y)d (y) : 8(x, y), f(x) + g(y) 6 c(x, y) <latexit 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<latexit 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<latexit sha1_base64="ioY1VH35aruLw9CJavGGunxImrM=">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</latexit> Wc(↵, ) = min ⇡2M+(X⇥Y) {hc, ⇡i : ⇡1 = ↵, ⇡2 = } <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="nYM/jZlh7URYT91c/XWPuQEUEDg=">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</latexit> Theorem: <latexit 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<latexit 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<latexit sha1_base64="TfxVz7U9ZiSc7OyPcRoyjTWz4r8=">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</latexit> Wc(↵, ) = max f2C(X),g2C(Y) {hf, ↵i + hg, i : f g 6 c} <latexit 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<latexit 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<latexit 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(see later) sup
  10. Continuous Dual Problem hf, ↵i def. = Z X f(x)d↵(x)

    <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="se5IX5+6njWKy85BP15PzazVNiY=">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</latexit> ↵ = P i ai xi <latexit 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<latexit 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sha1_base64="he7kQ98qCVO2MLGOmG/ISS/zGmM=">AABFzXictVzdchPJFW42fwv5Y5PLVKoma0ixKUJsZ1NJZWurFmxjvAhskGxYELj0MxYCSSMkjTAI5yYXeZbcJg+Q58gbJFd5hZyf7ukeqWdOj0OYst3T0985p890nz7ndA/t8aA/na2v//PCR9/69ne++72PL176/g9++KMfX/7kJ0fTJJ104sNOMkgmj9utaTzoj+LDWX82iB+PJ3Fr2B7Ej9qvtvD5o3k8mfaTUWP2dhw/G7Z6o/5Jv9OaQdXx5Z9fabYG0ZdRc5oOj/tRs4W/uvHx4vS4f3bl+PLa+o11+hetFjZ0YU3pfwfJJ5/WVFN1VaI6KlVDFauRmkF5oFpqCtdTtaHW1RjqnqkF1E2g1KfnsTpTlwCbQqsYWrSg9hX87sHdU107gnukOSV0B7gM4GcCyEhdBUwC7SZQRm4RPU+JMtYW0V4QTZTtLfxta1pDqJ2pF1Ar4UzLUBz2ZaZO1B+oD33o05hqsHcdTSUlraDkkdOrGVAYQx2Wu/B8AuUOIY2eI8JMqe+o2xY9/xe1xFq87+i2qfo3SXkVrkjVde+TjEJLzYl+RG8zhWcszwA494BCrPuIpTek6yH1fgTtF1B/H64zKhmdtOFaUO1ZKXILLh9yS0TuwuVD7orIGlw+ZE1EHsDlQx5oJGInpHM/vg6XD18XOT+Ay4d8ICIfwuVDPhSRR3D5kEci8glcPuQTEXkbLh/ytoi8C5cPeVdENuDyIRsi8hAuH/JQRO7A5UPuaGTxTJ3AlRCdvjArb0I5zwMtxQBqbory3SLr6MPeCpjTnQKsPKu34a8fux2g07gAuxMw7k4KsPLI2wUb6cfKtugOrSY+7B0RuwcjwI/dE7Ffq5cF2K8DZtqrAqw812rQzo+Vre89uPNj74nY+1DyY+U1ah9q/Nj9gBVjXIA9ELEP1OsCbIjVnxRgZbtfB7vix8rrVAPa+7Eh1jQtwMr29Ag8GD9WXq0eQa0f+0jEPlanhMWy9VEX5AWgJVul+ZhollP9Buy+jyr6ZSlZuVW63wTQfaLeFfTUrMyXaN3pkfwxzPMyaq1sLmNpDNRaAv9BtiINyKNuQ72E6WWYHmGGImI3Q+wGImoZohYs1zSzvlPykmUu9QxRD0S0sxUNSzOxfTdrj6VBAGI7Q2wvIcr8WHzXpi9z8klMjYScZesdlkL6lGRWH0uxHg/l9tog9nMIHtsvaORfpxgL4y7UVBm1F5lnwMiI7ssQbyjmM700PGTcTNuSPOpURLU9qLaIeutBvRVRqQeViqi5BzUXUXbmu7hmwAiw+sd3saA7HgHsWRdfEfgSN2GtugNzNILxcwC+40Oq2Ye/dYrYpatMMswB4OqKuZFnOUs8gdJCrUG9jSW3KSof0AyLQTJuua8zA3jH6wLPObbCZ9n6H2V5lnA6fZKnl9FBHzOi+VSNzl2qOSOfkEvV8HeyeW9K1fA7pPEz8v25VA0/09LPziF7Q2Mb58DWYTaNtfZtuSoNztowDVO+RKsuWlx8q0M9ZpDeaUX6e/rN7J3jvWxRifVjy9VoTJ3+TXP9q0LD6nnq6LkaFfSe2Fc2pahyT0Y6WrblqjIktIqOtBz2ruqbwTZd/WZMuRqNA/C4tihSXzjlqqN3nPXGlqvROFKcLT0j/9+Uq9Ho0T3rw5ar0cAcTUtnB2y5qmVHDXDEbctVrfqIcseYOeIxzzXWK5qQn5Rqan3yD8pzPK7Pv7qOYabneRYjlFOyvm0xnXa2lpVLZPyFGKzarKIc6F+kjg+Wp7FQm2J8xTLMcuv7Kh27xqPma6DFCGY/7xxImXaM/0wmA633AChuiFFXvmcGtynicJScLKGaunYmeouWL+ea8nXHVCvFZba3Vo9NstdTGntj8glrpFlJD7XCN1xEUdJQLachmV4V3b3T8zWv/XURN15CjLOR1qF9JN5/K49TfVqvOzq+qveGZnDxTpEdv5ijPtHWBmOehGwRylLG021nsk9uHa6r15XNjPOziN4o2qs5WY0+7WNNxSjU5JjZG1/QvaV9SDt5yINpdOA9RprKWPFeG+beMQsfkUV17a3EG/Vl8npcnpLVNfa4HN1z0D0PunqMswUrxn0oNSBmOIS7RkCUcynTVUIan6hfZ3uqCb3B8oh+kLOQhgbbmzhnIcui7Bc5Km8AjaOBo/RwGst0DL65QkmO+n3y2Ng1b/mv0n6v2RVv0RgvHs3FmZgucd0krhHNGt4L5rtlDizBwvtkk/zX8l4ivyoc0YZKXJ87nFkvIzonEFMEOybPeECzTZod+dZufmr5ieF0oMyOO+6BJ2QhI7J/EaxPCY3JiH7cEwdm350twoBsZIjd6Wfejc/X6YtjzPpxfcVnIex4i8mWpcTf0HVn15TGIkcMvA6cLY1to5Ma+YIxcZ1o627ndvnqg0h7usIdJUzRjpVrxP8z+m1+zDhZWxkRqGF8A1Nt63zvI6GYBXXUolW+3AaZtq6UVzIZnmup7fpnZbqSk2ybIi6UB1frLnDu0D3zwlEyIbmnK214HS3L5iLl8ZIesbcnFMWz3e/pFRjlvk6r5BrNuSaNkh6MglkWRZi2UhZ5mW85rzz1MNrT/wt1q+u81pBipGwGlzUk5fdjitZcKQcwqnn8vqLZ5Nf6ZKlVOZ8RjcWhM5ffQ+0v4LeR29yH0WnnrMItGgNMwd5ZjXBNtNIijNetHC8zMg0te2/52TFpWrk154mv2brZGHtemcoBjZpTnbUw5fPQeOnQeBmowwbtUFotmnpjiY7F2KKh9zhD+VXh1qhAORUpyx6ZQfUDpHRjqTCqXZGqHOMb1DuR1rpIqwWz1d0NcOd8CNI/15dn9/tsdY/UbfJtOuSBcfzSpVnaJ5/L1JZHakwBOX+u7as7+5tUg9zbZEGRMp/+xBnDu04dus4ySX+pV7aE7Ly1COa00xvdxtjYJpV/u4Ic0pyY0rw0iM+pRazld+WIlizSDcfniCjz3yKfiv2O8pjZbW3fSZTzJ2y8ybPK8uJIYUT6lzJveyvR654Tv0YUE6bau24DrepvGCkwxmQS/J7llN4QrnK8k8AebZvs56qd4l28kSPRDZJ6ob4MsDEc9dqx7o4t02PTt19BS9S6feu+FjK/QTBHid95dvRatKoNtY+6WLo/H62WXuXy92V6SJf4Wn2k1MaNLGyUl8c01RfBXFiialwYE8KlWi+qyF9N8ioy8+5UKGXT2lDOZxrYxrygeEk6PYoIn3d3zevNfSb0o71Cr01YlxrXSJQwG5fo/IBraTErdXFlHeLai6Wr0cBZiYpWCkPdXS2s/WYLGZP1GygpZ8OtXdmbuShFzsIwhY7ic8BF8aFL8wv1R/odKV90aDiG5A7r4N/eVFtq5wOchnity5zRjKgGbUF3KfZu6X7mW5Tr6LVD3aUfwiGcRx90LUnfp5W0quxMWZbcpR5O/w1ZgYmKRelty+p9cLnIPVnlVKU/fbJscm/6ynzBU7UvhkNIT/JcwvnwvobUixNlvoSq1gdDXe5BnkMVHuYcQ9g7t62r83I5letrlUsoD14FzI6LweHOX3GsYtuFWKiJ80Y+PAe0Dicl1M1q8b/2w/CxnKrzCuU2pS/UXga8dW4X64ws+sPV54zlFjKaizmG80yy3llvyc+P/b6o0ptKnN58eProj9oxYHgtFOdBZekY744iK28oFdwX8MmQqP+of1yQv2F4ndEokqMKJbNPUUzNtJCpme80fb0zz0JksnSKZMpTs3FEnU7Ebqk9dRt+tjIPsOrpUP4Ck/8i1v/VbRdqT8h6mCw6Zw6aVBdT9sPuonXp3p6fLZIYz/Ly2d4G1OBeeI1q8ZzvfWqPZ30bub4Vf3fCc/2eSlQ3F5Es7+7ZedWGHuR33jgHZL4OjugsPWex+OTZMGBvkc9PcYTk+w5lWdIFIcxoKaPc9lJ2v0VZpd3O9a1DI3ysd/hxvwHP5beyrFKkfkN1Lb064EotSXXgkeopZQTapP91iNB+p67D3+u67Jf0QMnZpzHItHUufuNsV9foYUpvON/fU+dZ+fmyM++os19WXqXsmsn/zXW7hHIFdk+yPL+7XciFz9GX43sl+J4jZZ3GwiuK5ieqPCOZltBMtUzuLvFImWwq6wFj5VY2+sqj83kJr3lA/+8Wou86ku6CLG3K4Ue0SzghegOtmx2Snk9rlmeD75RIa74gZZr2vKYdB+bkZflOw8A79l3bwqcrpQxQXEDHtSR8zlO2SeasZ7lM5nxqiI2Lg2SbOfSKZZP1JWsrRFcSlVSUJA34rnoeIMs8gM6JIM2JSKEnSqItzPHltY3l/7lktXC0eWNj/cbGg821r27p/9XkY/Uz9am6Bmvz79VXMIMO1CFw+rP6q/qb+vvO/k66837nT9z0owsa81OV+7fzl/8CLAx05Q==</latexit> f = (f(xi))i <latexit 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<latexit 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<latexit sha1_base64="FXXrDSJSbBUCdTCgZ7J0/L8mavc=">AABF6HictVxLkxPJES7WrwW/WPvoS3sHHODAeGa8Dm94YyMWZgaYRcCANAMLggk9WkKgUQu1JIbV6j/45vDFB/8RX3y17/4H9sl/wfmo6qqWqjurx5iOmamuri8zK7sqKzOrmvZ4OEinm5v/PPfBt779ne9+78PzF77/gx/+6McXP/rJUZrMJp34sJMMk8mTdiuNh4NRfDgdTIfxk/Ekbp20h/Hj9usdfP54Hk/SQTJqTN+N4+cnrf5o0Bt0WlOoOr746aVFk6gsJnF3GTWP4s70XtKNF73lMvo8uuI+7S2vnB4Prl49XgyWl44vbmxe36R/0XphSxc2lP53kHz0cU01VVclqqNm6kTFaqSmUB6qlkrheqa21KYaQ91ztYC6CZQG9DxWS3UBsDNoFUOLFtS+ht99uHuma0dwjzRTQneAyxB+JoCM1GXAJNBuAmXkFtHzGVHG2iLaC6KJsr2Dv21N6wRqp+ol1Eo40zIUh32Zqp76lPowgD6NqQZ719FUZqQVlDxyejUFCmOow3IXnk+g3CGk0XNEmJT6jrpt0fN/UUusxfuObjtT/yYpL8MVqbrufZJRaKk50Y/obc7gGcszBM59oBDrPmLpLen6hHo/gvYLqL8P15JKRidtuBZUuyxF7sDlQ+6IyNtw+ZC3RWQNLh+yJiIP4PIhDzQSsRPSuR9fh8uHr4ucH8LlQz4UkY/g8iEficgjuHzIIxH5FC4f8qmIvAWXD3lLRN6Fy4e8KyIbcPmQDRF5CJcPeSgi9+DyIfc0snimTuBKiM5AmJU3oJzngZZiCDU3RPluknX0YW8GzOlOAVae1bvw14/dDdBpXIDdCxh3vQKsPPJug430Y2VbdIdWEx/2jojdhxHgx+6L2C/VqwLslwEz7XUBVp5rNWjnx8rW9x7c+bH3ROx9KPmx8hr1AGr82AcBK8a4AHsgYh+qNwXYEKs/KcDKdr8OdsWPldepBrT3Y0Os6awAK9vTI/Bg/Fh5tXoMtX7sYxH7RJ0SFsvWR12QF4CWbJ3mE6JZTvUrsPs+quiXzcjKrdP9KoDuU/V1QU/NynyB1p0+yR/DPC+j1srmMpbGQK0l8B9mK9KQPOo21EuYfobpE+ZERNzOELcDEbUMUQuWK82sb0pessylniHqgYh2tqJhaSq272btsTQMQOxmiN0VRJkfi+/a9GVOPompkZDTbL3DUkifkszqYynW46HcXhvEgxyCx/ZLGvnXKMbCuAs1VUbtZeYZMDKi+zLEW4r5TC8NDxk31bYkjzoVUW0Pqi2i3nlQ70TUzIOaiai5BzUXUXbmu7hmwAiw+sd3saA7HgHsWRdfEfgSN2CtugNzNILxcwC+4yOqeQB/6xSxS1eZZJgDwNUVcyPPc5Z4AqWF2oB6G0vuUlQ+pBkWg2Tc8oHODOAdrws859gKL7P1P8ryLOF0BiRPP6ODPmZE86kanbtUsySfkEvV8HeyeW9K1fB7pPEl+f5cqoafaumnZ5C9obGNM2DrMJvGWvu2XJUGZ22YhilfoFUXLS6+1RM9ZpDeaUX6+/rN7J/hvexQifVjy9VopE7/0lz/qtCwek4dPVejgt4T+8qmFFXuyUhHy7ZcVYaEVtGRlsPeVX0z2Kar34wpV6NxAB7XDkXqC6dcdfSOs97YcjUaR4qzpUvy/025Go0+3bM+bLkaDczRtHR2wJarWnbUAEfctlzVqo8od4yZIx7zXGO9ogn5STNNbUD+QXmOx/X519cxzPS8yGKEckrWty2m087WsnKJjL8Qg1WbVpQD/YuZ44PlaSzUthhfsQzT3Pq+Tseu8aj5GmgxgtnPOwdSph3jP5PJQOs9BIpbYtSV75nBbYs4HCW9FVRT105Fb9Hy5VxTvu6YaqW4zPbW6rFJ9jqlsTcmn7BGmpX0UCt8w0UUJQ3VchqS6VXR3dd6vua1vynixiuIcTbSOrSPxPtv5XGqT+t1R8eX9d7QFC7eKbLjF3PUPW1tMOZJyBahLGU83XYm++TW4bp6TdnMOD+L6I2ivZqT1RjQPlYqRqEmx8ze+ILuLe1D2slDHkyjA+8x0lTGivfaMPeOWfiILKprbyXeqC+T1+NySlbX2ONydN9B9z3o6jHODqwY96HUgJjhEO4aAVHOhUxXCWl8on6V7akm9AbLI/phzkIaGmxv4pyFLIuyX+aovAU0jgaO0sNprNIx+OYaJTnq98ljY9e85b9M+71mV7xFY7x4NBdnYrrEdZu4RjRreC+Y71Y5sAQL75Nt8l/Le4n8qnBEGypxfeFwZr2M6JxATBHsmDzjIc02aXbkW7v5qdUnhtOBMjvuuAeekIWMyP5FsD4lNCYj+nFPHJh9d7YIQ7KRIXZnkHk3Pl9nII4x68cNFJ+FsOMtJls2I/6Grju7UhqLHDHwOrBcGdtGJzXyBWPiOtHW3c7t8tUHkfZ0hTtKmKIdK1eI/1X6bX7MONlYGxGoYXwDqbZ1vveRUMyCOmrRKl9ug0xbV8pLmQwvtNR2/bMyXcpJtksRF8qDq3UXOHfonnnhKJmQ3OlaG15Hy7K5SHm8okfsbY+ieLb7fb0Co9zXaJXcoDnXpFHSh1EwzaII01bKIq/yLeeVpx5GO/2/ULe6zmsNKUbKZnBZQ1J+P6ZozZVyCKOax+9rmk1+rU9WWpXzGdFYPHHm8jdQ+3P4beQ292F02jmrcJPGAFOwd1YjXBOttQjjdTPHy4xMQ8veW352TJpWbs1Z4mu2bjbGnlemckCj5lRnLUz5LDReOTReBeqwQTuUVoum3liiYzG2aOg9zlB+Vbg1KlCeiZRlj8ygBgFSurFUGNWuSFWO8Q3qa5HWpkirBbPV3Q1w53wI0j/XV2f3N9nqHqlb5Nt0yAPj+KVLs3RAPpepLY/UmAJy/kTbV3f2N6kGubfJgiJlPv2JM4Z3nTp0LTNJf6FXtoTsvLUI5rTTW93G2NgmlX+zhjyhOZHSvDSIT6hFrOV35YhWLNJ1x+eIKPPfIp+K/Y7ymNltbd9JlPMnbLzJs8ry4khhRPqXMm/7a9HrvhO/RhQTzrR33QZa1d8wUmCMyST4PcuU3hCucryTwB5tm+znup3iXbyRI9F1knqhPg+wMRz12rHuji3TY9O3X0JL1Lp9674WMr9hMEeJ31l29Fq0qp1oH3Wxcn82Wi29yuXvy/QwW+Fr9TGjNm5kYaO8PKapPgvmwhJV48KYEC7VelFF/mqSV5GZd6dCKZvWhnI+08A25iXFS9LpUUT4vLsrXm/uqtCP9hq9NmFdalwjUcJsXKLzA66lxazU+bV1iGvPl65GQ2clKlopDHV3tbD2my1kTNZvqKScDbd2ZW/mohQ5C8MUOorPARfFhy7Nz9Tv6XekfNGh4RiSO6yDf3tD7ai993Aa4o0uc0Yzohq0Bd2V2Lul+5lvUa6jNw51l34Ih3AeA9C1JP2AVtKqsjNlWXKXejj9t2QFJioWpbctq/fB5SL3ZJ1Tlf4MyLLJvRko8wVP1b4YDiE9yXMJ58P7GlIvesp8CVWtD4a63IM8hyo8zDmGsHduW1fn5XIq19c6l1AevAqYHReDw52/4ljFtguxUBPnjbx/DmgdeiXUzWrxv/bD8LGcqvMK5ZbSF2qvAt46t4t1Rhb94epzxnILGc3FHMN5JlnvrLfk58d+X1TpTSVOb94/ffRH7RgwvBaK86CydIx3R5GVN5QK7gv4ZEjUf9Rfz8nfMLzJaBTJUYWS2acopmZayNTMd5q+3plnITJZOkUy5anZOKJOJ2J31L66BT87mQdY9XQof4HJfxHr/+q2C7U9sh4mi86ZgybVxZT9sLtoXbq352eLJMazvHy2twE1uBdeo1o853uf2uNZ30aub8XfnfBcv6cS1c1FJKu7e3ZetaEH+Z03zgGZr4MjOkvPWSw+eXYSsLfI56c4QvJ9h7Iq6YIQZrSUUW57KbvfoqzTbuf61qERPtY7/LjfgOfyW1lWKVK/prqWXh1wpZakOvBI9YwyAm3S/yZEaL9V1+DvNV32S3qg5OzTGGTaORO/cbara/SQ0hvO9/fUeVZ+vmzpHXX2y8rLlF0z+b+5bpdQrsDuSZbnd3cLufA5+nJ8vwTfd6Ss01h4TdH8RJVnJGclNGdaJneXeKRMNpX1gLFyKxt95dH5vITXPKD/dwvRdx1Jb4MsbcrhR7RLOCF6Q62bPZKeT2uWZ4PvlEhrviBlmva8ph0H5uRl+U7D0Dv2XdvCpyulDFBcQMe1JHzOU7ZJ5qxnuUzmfGqIjYuDZJs69Iplk/UlaytEVxKVmSjJLOC76nmALPMAOj1Bmp5IoS9Koi3M8cWNrdX/uWS9cLR9fWvz+tbD7Y0vbur/1eRD9TP1sboCa/Pv1Bcwgw7UIXD6s/qb+rv6x96rvT/s/XHvT9z0g3Ma81OV+7f3l/8CpI2BFQ==</latexit> hf, ai def. = P i fiai <latexit 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<latexit 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<latexit sha1_base64="JiXKd22Cbax9asEhjpJf4ehSfA0=">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</latexit> max f2C(X),g2C(Y) ⇢Z X f(x)d↵(x) + Z Y g(y)d (y) : 8(x, y), f(x) + g(y) 6 c(x, y) <latexit 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<latexit 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<latexit 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Primal-dual relations: <latexit 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<latexit 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Supp(⇡) ⇢ {(x, y) : f(x) + g(y) = c(x, y)} <latexit 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<latexit 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<latexit 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Wc(↵, ) = min ⇡2M+(X⇥Y) {hc, ⇡i : ⇡1 = ↵, ⇡2 = } <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="nYM/jZlh7URYT91c/XWPuQEUEDg=">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</latexit> Theorem: <latexit 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<latexit 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<latexit sha1_base64="TfxVz7U9ZiSc7OyPcRoyjTWz4r8=">AABFP3ictVxLcxu5EYY3r7U3Dzs55jJZrVPelONIyqaS2q1UrS3KttZaWzYp2bum7eJjSNEecmi+JJurn5Jr8jNS+Rn5BUkuSa65pR/AAENipjGK4ylJGBBfd6MBNLoboNvjZDCdbW7+9cJ73/r2d777vfcvXvrg+z/44Y8uX/nx0TSdTzrxYSdN0smTdmsaJ4NRfDgbzJL4yXgSt4btJH7cfrWDnz9exJPpIB01Zm/G8bNhqz8a9Aad1gyqXly+0pzFp4BbNo7jdBIPPz17cXlj88Ym/YvWC1u6sKH0v4P0yocfqKbqqlR11FwNVaxGagblRLXUFJ6nakttqjHUPVNLqJtAaUCfx+pMXQLsHFrF0KIFta/gdx/enuraEbwjzSmhO8AlgZ8JICN1FTAptJtAGblF9PmcKGNtEe0l0UTZ3sDftqY1hNqZOoZaCWdahuKwLzPVU7+jPgygT2Oqwd51NJU5aQUlj5xezYDCGOqw3IXPJ1DuENLoOSLMlPqOum3R53+nlliL7x3ddq7+QVJehSdSdd37NKPQUguiH9FozuEzlicBzn2gEOs+YumEdD2k3o+g/RLq78NzRiWjkzY8S6o9K0XuwOND7ojIO/D4kHdE5D48PuS+iDyAx4c80EjETkjnfnwdHh++LnJ+CI8P+VBEPoLHh3wkIo/g8SGPROTX8PiQX4vI2/D4kLdF5D14fMh7IrIBjw/ZEJGH8PiQhyJyFx4fclcji1fqBJ6U6AyEVXkTynkeaCkSqLkpyneLrKMPeytgTXcKsPKqrsFfP7YWoNO4ALsbMO96BVh55t0BG+nHyrboLu0mPuxdEbsHM8CP3ROxX6iXBdgvAlbaqwKsvNb2oZ0fK1vfL+HNj/1SxN6Hkh8r71EPoMaPfRCwY4wLsAci9qF6XYANsfqTAqxs9+tgV/xYeZ9qQHs/NsSazguwsj09Ag/Gj5V3q8dQ68c+FrFP1GkB9omI/Qqsux/7VcAO+7YAa/bYS7SD9MkfiWHFllFrZasSS2Og1hL4J9nekpBv3IZ6CdPPMH3CDEXEnQxxJxCxnyH2g+WaZnZ0Sv6uzKWeIeqBiHa2N2FpJrbvZu2xlAQgahmitoIo80hxrE1fFuRdmBoJOct2LiyF9CnN7DeWYj0fyi2vQTzIIXhuH9PMv07REkZQqKkyasfZHs/IiN7LECcUvZleGh4ybpZZBRd1KqLaHlRbRL3xoN6IqLkHNRdRCw9qIaLsyndxzYAZYPWPY7GkN54B7CMXPxF4BTdh17kLazSC+XMAXuAjqnkAf+sUe0tPmWQYzeM+iVmOZzlLPIHSUm1AvY0KaxRfJ7TCYpCMWz7QMT6+YW5jqdccW+GzbCePsoxJOJ0BydPP6KC3GNF6qkbnHtWckXfHpWr4u9m6N6Vq+F3S+Bl58Vyqhp9p6WfnkL2hsY1zYOuwmsZa+7ZclQbnX5iGKV+iXRctLo7qUM8ZpHdakf6eHpm9c4zLDpVYP7ZcjcbU6d80178qNKyep46eq1FB74m9XlOKKvdkpONeW64qQ0q76EjLYd+qjgy26eqRMeVqNA7A49qhmHvplKvO3nHWG1uuRuNIcd7zjDx5U65Go0/vrA9brkYDsy0tHefbclXLjhrg2NmWq1r1EWWBMQfEc55rrFc0IT9prqkNyD8oz9a4Pv/6PoY5m+dZjFBOyfq2xXTa2V5WLpHxF2KwarOKcqB/MXd8sDyNpdoW4yuWYZbb39fp2D0eNb8PWoxg9fMZgJQzT0BCk5NA650AxS0x6sr3zOC2RRzOkt4KqqlrZ6K3aPly1ihf94JqpbjM9tbqsUn2ekpzb0w+4T5pVtLDfuEIF1GUNLSf05BMr4ru3ur1mtf+pogbryDG2Uzr0IkQn6SVx6k+rdcdHV/VpzwzePjMx85fzDb3tLXBmCclW4SylPF025k8kluH++p1ZXPc/FlEI4r2akFWY0AnUlMxCjXZYvbGl/RuaR/SmRzyYBodGMdIUxkrPjXDLDrm0yOyqK69lXijvkyGjstTsrrGHpej+w6670FXj3F2YMe4D6UGxAyH8NYIiHIuZbpKSeMT9cvsdDSlESyP6JOchTQ02N7EOQtZFmUf56icABpnA0fp4TRW6Rh8c42SHPX75LGxa97yX6WTW3O+3aI5XjybizMxXeK6TVwjWjV8qstvqxxYgqX3k23yX8t7ifyqcEQbKnF97nBmvYzoxD+mCHZMnnFCq01aHfnWbn5q9RPD6UCZs3M8zU7JQkZk/yLYn1KakxH9uHcHzAk6W4SEbGSI3Rlk3o3P1xmIc8z6cQPFtxrsfIvJls2Jv6Hrrq4pzUWOGHgfOFuZ20Yn++QLxsR1oq27Xdvluw8i7T0Jd5YwRTtXrhH/j+m3+THzZGNtRqCGcQSm2tb5xiOlmAV11KJdvtwGmbaulB9lMjzXUtv9z8r0UU6yGkVcKA/u1l3g3KF35oWzZEJyT9fa8D5als1FyuMVPWJvexTFs93v6x0Y5b5Ou+QGrbkmzZI+zIJZFkWYtlIWeZVvOa889TDa0/8LdavrvNaQYqRsBpc1JOX3Y4rWXCkTmNU8f1/RavJrfbLSqpzPiObi0FnL30Dtz+C3kdu8h9Fp56zCLZoDTMG+WY1wTbTWIozXrRwvMzMNLftu+dk5aVq5NeeJr9m62Rh7UZnKAc2aU521MOXz0Hjp0HgZqMMGnTVaLZp6Y4leiLFFQ59WhvKrwq1RgfJcpCx7ZAY1CJDSjaXCqHZFqnKMb1BvRVqbIq0WrFb3NMBd8yFI/1pfXd3fZLt7pG6Tb9MhD4zjly6t0gH5XKa2PFJjCsj5E21f3dXfpBrk3iYLipT5HieuGD516tBzlkn6c72zpWTnrUUw95ZOdBtjY5tU/vUackhrYkrr0iA+oRaxlt+VI1qxSDccnyOizH+LfCr2O8pjZre1HZMo50/YeJNXleXFkcKI9C9l3vbWotc9J36NKCaca++6DbSqjzBSYIzJJPg9yymNEO5yfJLAHm2b7Oe6neJTvJEj0Q2Seql+H2BjOOq1c92dW6bHpm+/gJaodTvqvhYyvySYo8TvPCd6LdrVhtpHXa68n49WS+9y+fcyPcxX+Fp9zKmNG1nYKC+PaarPgrmwRNW4MCaES7VeVJG/muRVZObTqVDKprWhnM80sI05pnhJugeKCJ93d83rzX0s9KO9Rq9NWJca10iUMBuX6vyAa2kxK3VxbR/i2oulu1Hi7ERFO4Wh7u4W1n6zhYzJ+iVKytlwa1f2Zi5KkbMwTKGj+EZvUXzo0vxMfUq/I+WLDg3HkNxhHfzbm2pH7b6D2xCvdZkzmhHVoC3orsTeLd3PfItyHb12qLv0QziE8xiAriXpB7STVpWdKcuSu9TD6Z+QFZioWJTetqzeB5eL3JN1TlX6MyDLJvdmoMx3car2xXAI6UmeSzgfPteQetFT5jtN1fpgqMs9yHOowsPcYwgbc9u6Oi+XU7m+1rmE8uBdwJy4GBye/BXHKrZdiIWaOCPy7jmgdeiVUDe7xf/aD8PHcqrOK5TblL5r9jJg1LldrDOy6A9XXzOWW8hsLuYYzjPNeme9JT8/9vuiSiOVOr159/TRH7VzwPBaKs6DytIx3p1FVt5QKngu4JMhVf9Sf74gfxvhdUajSI4qlMw5RTE100KmZr5x6eud+SxEJkunSKY8NRtH1OlG7I7aU7fhZyfzAKveDuXvUvJfxPq/P9uF2h5ZD5NF58xBk+piyn7YU7Quvdv7s0US411evtvbgBo8C9+nWrzne5/a413fRq5vxd8g4bX+pUpVNxeRrJ7u2XXVhh7kT944B2S+5xvRXXrOYvHNs2HA2SLfn+IIyXzreUmILsWDq5IuCWFmSxnltpdym+4ixQW0207fyrOJVaXuKTlb1D+HxP3caHRoTY71nQQ8IcFvErSyPFikfkV1Lb2foW8h6fHAI9VTymG0acZsQkz5G3Ud/l7XZb+kB2uSTmnW5CU6dT4rv7N25p3J9nuXVyljZ3KKC90upfyDPecsH+VaIRcez3J8vwTfd6Ss02i9ogzBRJVnOeclNOdaJvfkeaRMhpb1gPF3K5sf5RH/ooTXIqD/9wrR9xxJ74AsbToXiOjkcUL0Eq2bXZKeb4CWZ5jvlkhrvl/KNO0dUDsPzG3O8tOLRM+74pXPNzalrFJcQMdd63x3VDpPkeWRpQmRRaIyFyWZB3yreREgyyKATk+QpidS6IuS6BX84vLG1ur/G7JeONq+sbV5Y+vh9sbnt/T/KfK++qn6UF2D/fS36nOYoQfqEDidqD+oP6o/1f5S+1vtn7V/c9P3LmjMT1TuX+0//wVL2FnL</latexit> Wc(↵, ) = max f2C(X),g2C(Y) {hf, ↵i + hg, i : f g 6 c} <latexit 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<latexit 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<latexit 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(see later) sup
  11. C-transforms Fixing f, solve the dual with respect to g:

    <latexit sha1_base64="izjhNSpYSgi9QeTHRhVJz7BqTyg=">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</latexit> <latexit sha1_base64="izjhNSpYSgi9QeTHRhVJz7BqTyg=">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</latexit> <latexit 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<latexit sha1_base64="izjhNSpYSgi9QeTHRhVJz7BqTyg=">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</latexit> max g2C(Y) ⇢Z Y g(y)d (y) : 8(x, y), f(x) + g(y) 6 c(x, y) <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="Ctw3wt9QBMWIGiay2Uv+mTIA6qs=">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</latexit> max g2C(Y) ⇢Z Y g(y)d (y) : 8y, g(y) 6 min x c(x, y) f(x) <latexit 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<latexit 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<latexit 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  12. C-transforms Fixing f, solve the dual with respect to g:

    <latexit sha1_base64="izjhNSpYSgi9QeTHRhVJz7BqTyg=">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</latexit> <latexit sha1_base64="izjhNSpYSgi9QeTHRhVJz7BqTyg=">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</latexit> <latexit 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<latexit sha1_base64="izjhNSpYSgi9QeTHRhVJz7BqTyg=">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</latexit> max g2C(Y) ⇢Z Y g(y)d (y) : 8(x, y), f(x) + g(y) 6 c(x, y) <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="Ctw3wt9QBMWIGiay2Uv+mTIA6qs=">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</latexit> max g2C(Y) ⇢Z Y g(y)d (y) : 8y, g(y) 6 min x c(x, y) f(x) <latexit 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<latexit 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<latexit 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c-transforms: <latexit 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<latexit 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<latexit 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fc(y) def. = min x2X c(x, y) f(x) <latexit 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<latexit 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<latexit sha1_base64="KTePQAfBrlkXL99fiykWcKDj/c4=">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</latexit> gc(x) def. = min y2Y c(x, y) g(y) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  13. C-transforms Fixing f, solve the dual with respect to g:

    <latexit sha1_base64="izjhNSpYSgi9QeTHRhVJz7BqTyg=">AABFp3ictVzvctu4EUeuf+6S/su1H/uFPSedpOPmbN912rmbzlxiO44vTuxEspNLlGQoiZKZ0KIiUrITnZ+jT9Ppt/YZ+gbtp75CdxcAAUogF3TTcGyDIH67iyWw2F2A6Y6TOMvX1v556aMf/PBHP/74k8tXfvLTn/38F1c//eVRlk4nveiwlybp5Gk3zKIkHkWHeZwn0dPxJApPukn0pPtmE58/mUWTLE5H7fzdOHpxEg5H8SDuhTlUvbq6fjc+i0fD4FpncG01yNJkFgX5cRT0p2ESnMb5cTCJsnHUy4M8hUbDa1+9urqydmuN/gXLhXVVWBHq30H66Wefi47oi1T0xFSciEiMRA7lRIQig+u5WBdrYgx1L8Qc6iZQiul5JM7FFcBOoVUELUKofQO/h3D3XNWO4B5pZoTuAZcEfiaADMR1wKTQbgJl5BbQ8ylRxtoq2nOiibK9g79dResEanNxDLUcTrf0xWFfcjEQf6I+xNCnMdVg73qKypS0gpIHVq9yoDCGOiz34fkEyj1Caj0HhMmo76jbkJ7/i1piLd73VNup+DdJeR2uQLRU79OCQihmRD+gtzmFZ1KeBDgPgUKk+oilU9L1CfV+BO3nUP8QrnMqaZ104ZpT7XktchMuF3KTRe7A5ULusMg9uFzIPRZ5AJcLeaCQiJ2Qzt34FlwufIvl/AguF/IRi3wMlwv5mEUeweVCHrHIZ3C5kM9Y5F24XMi7LPI+XC7kfRbZhsuFbLPIQ7hcyEMWuQ2XC7mtkNUzdQJXSnRiZlbehnKZB1qKBGpus/LdIevowt7xmNO9Ciw/q7fgrxu75aHTqAK77THuBhVYfuTtgI10Y3lbdI9WExf2HovdhRHgxu6y2G/F6wrstx4z7U0Flp9re9DOjeWt7wO4c2MfsNiHUHJj+TVqH2rc2H2PFWNcgT1gsY/E2wqsj9WfVGB5u98Cu+LG8utUG9q7sT7WdFqB5e3pEXgwbiy/Wj2BWjf2CYt9Ks4Ii2Xjo87JC0BLtkzzKdGsp/od2H0XVfTLpmTllul+50H3mXhf0VO9Ml+hdWdI8kcwz+uohWouV/cdW4yBS8hKlhRrVUK+dhfqQwYzLDBDwpywiJ0CseOJ2CsQe95yZYVdzsh/5rm0CkTLE9FVa13dCME2uYfu+8W6iaVEYepXaY3YWkDUeb84EnQ/Z+TJ6BoOmRerJJYiDwnTYq3AUqTGSr2V14j9EkLOiGOaL6sUmWG0hpqqo3Zc+BMSGdB9HeKUIkXdS82Dx+XKApVRZyyq60B1WdQ7B+odi5o6UFMWNXOgZizKWAUb1/EYAUb/+C7mdCdHgPTHq68APJDbsMLdg/kbwPg5AI/zMdXsw98WxfncVScZZg5wTcaMyouS/Z5AaS5WoN5EoFsUyyc0wyKQTLbcV/kEvJO2Qs45aaPPC68hKLIz/nRikmdY0EHPNKD51IzOfao5J09Slprh7xXzXpea4bdJ44jXpWb4XEmfX0D2tsK2L4BtwWwaK+2bclMaMtcjaejyFVqR0eLiWz1RYwbpnTWkv6vezO4F3ssmlaR+TLkZjczqX1bqXxMaRs+ZpedmVNDnkh62LgWNezJSMbYpN5UhpVV0pOQwd03fDLbpqzejy81oHIA3tknx/dwqNx2946I3ptyMxpGQOdZzihp0uRmNId1LfZhyMxqY2QlVTsGUm1p21ICM0025qVUfUcYZ801yzMsa4xVNyE+aKmox+Qf1mSE7IlhexzA/9FLoyKKekvFuq+l0i7WsXiLtL0Rg1fKGcqB/MbV8sDKNudhg/W8pQ15a35fpmDUeNb8HWgxg9sv9Bi4/jzGBzn+g9U6A4jobkZV7pnEbLA5HyWAB1VG1OestGr6viwjH1L2iWi5mM701euyQvc5o7I3JJ9wjzXJ62Kt8w1UUOQ3tlTTE02uiu/dqvpa1v8bixguIcTHSerT7JHft6mNYl9Zblo6vqx2lHC65v2TGL2a2B8raYMyTki1CWep42u10zsquw3V1VZh8unwW0BtFezUjqxHT7lfGRqE6My298TndG9qHtP+HPCSNHrzHQFEZC7lDhxl7zN0HZFFte8vxRn3pbKAsZ2R1tT2uRw8t9NCBbh7jbMKK8RBKbYgZDuGu7RHlXCl0lZLGJ+L3xU5sSm+wPqJPShZS05D2JipZyLoo+7hE5RTQOBpklO5PY5GOxneWKPFRv0seE7uWLf912iXWe+khjfHq0VydiekT1w3iGtCskTvI8m6Rg5Rg7nyyQf5rfS+RXxOOaEM5ri8tzlIvIzpdEFEEOybPOKHZxs2Ocms7P7X4RHM6EHqfHnfOU7KQAdm/ANanlMZkQD/2OQW9Wy8tQkI20sfuxIV34/J1YnaMGT8uFvIEhRlvEdmyKfHXdO3ZldFYlBGDXAfOF8a21ske+YIRcZ0o627mdv3qg0hzJsMeJZKiGSs3iP9N+q1/9DhZWRoRqGF8A5myda73kVLMgjoKaZWvt0G6rS3ltUKGl0pqs/4Zma6VJNuiiAvlwdW6D5x7dC954SiZkNzZUhu5jtZlc5HyeEGP2NsBRfHS7g/VCoxyr9IquUJzrkOjZAijIC+iCN2WyyIv8q3nVabuRzv7v1A3ui5rDSkGwmRwpYa43H9E0ZotZQKjWo7fNzSb3FqfLLSq5zOisXhizeXvofY38FvLre/96HRLVuEOjQFJwdwZjciaYKmFH687JV56ZGpa5t7wM2NSt7JrLhJfS+tmYuxZYyoHNGrOVNZCly9C47VF47WnDtu0r2m0qOu1JXrFxhZttTPqy68Jt3YDylOWMu+RaVTsIaUdS/lR7bNU+Rhfo96ztNZYWiHMVns3wJ7zPkj3XF+c3d8Xq3sg7pJv0yMPTMYvfZqlMflcurY+UpMUkPOXyr7as79DNci9SxYUKcszozhj5K5Tj67zQtLfqpUtJTtvLII+I3Wq2mgb26HyF0vIE5oTGc1LjfiSWkRKfluOYMEi3bJ8joAy/yH5VNLvqI+Z7dbmnQQlf8LEm3JWGV4yUhiR/rnM2+5S9Lprxa8BxYRT5V13gVbzN4wUJEZnEtyeZUZvCFc5uZMgPdou2c9lOyV38UaWRLdI6rn4s4eNkVGvGev22NI91n37HbRErZu37mrB80u8OXL8LrKjF9KqdqJ81PnC/cVohWqVK9/X6WG6wNfoY0pt7MjCRHllTEd87c1FStSMi8T4cGnWiybyN5O8icxyd8qXsm6tKZczDdLGHFO8xJ05RYTLu7vh9OZuMv3oLtHrEtamJms4SpiNS1V+wLa0mJW6vLQOydrLtatRYq1EVSuFpm6vFsZ+SwsZkfVLBJezka1t2TulKIXPwkgKPSFPD1fFhzbNr8VX9DsQruhQc/TJHbbAv70tNsX2BzgN8VaVZUYzoBq0Bf2F2DtU/Sy3qNfRW4u6Td+Hgz+PGHTNSR/TStpUdkmZl9ym7k//lKzARESs9KZl8z7YXPieLHNq0p+YLBvfm1jo736a9kVz8OlJmYs/H7mvwfViIPT3U836oKnzPShzaMJDn2Pwe+emdXNeNqd6fS1z8eUhVwG946JxuPNXHauYdj4WamK9kQ/PAa3DoIa6Xi3+135oPoZTc16+3DL6ru21x1uX7SKVkUV/uPmcMdx8RnM1R3+eadE74y25+Um/L2j0plKrNx+ePvqjZgxoXnMh86C8dBJvjyIjry8V3BdwyZCK/4i/XeK/fHhb0KiSowklvU9RTU234KnprztdvdPPfGQydKpkKlMzcUSLTsRuil1xF342Cw+w6elQ+d2m/ItY97e6fagdkPXQWXSZOehQXUTZD7OL1qd7c362SmI8yyvP9rahBvfC96gWz/k+pPZ41rdd6lv11ypyrj8QqeiXIpLF3T0zr7rQg/LOm8wB6W+KAzpLL7NY8uTZicfeojw/JSMk1xcci5LORShM3qWOctdJ2f4+YZl21+pbfTaxTmp9crt+RA8Z+ebUwmi6R/NtrM4b4O4HfiUQFjmuQHxOdaFaq9Bv4HR04JDhOeUnujQa1iBe/INYhb+rquzW28GSpBmNiLJEZ9az+vNo585Rar7fvE7ZOJ0vnKl2KeUWzB5m/RvcquQi3149fliDH1pStuhtvaHofyLqM5jTGppTJZO9qzwSOvsq9YCxdViMj/poflbDa+bR//uV6PuWpDsgS5dy/gHtKk6IXqJ0s03Sy9Od9dnjezXS6u9UJU1zvtOMA31Ss35nIlHjrtoWydOYXMYoqqCz+GUUv8vCy8NL4yMLR2XKSjL1+Dp65iHLzIPOgJFmwFIYspKoGfzq6sr64v8/slw42ri1vnZr/dHGyjd31P9N8on4tfhM3IC18o/iGxihB+IQOP1F/FX8Xfxj++b2/vbR9lPZ9KNLCvMrUfq3Hf4X7utxqQ==</latexit> <latexit sha1_base64="izjhNSpYSgi9QeTHRhVJz7BqTyg=">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</latexit> <latexit 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<latexit sha1_base64="izjhNSpYSgi9QeTHRhVJz7BqTyg=">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</latexit> max g2C(Y) ⇢Z Y g(y)d (y) : 8(x, y), f(x) + g(y) 6 c(x, y) <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="Ctw3wt9QBMWIGiay2Uv+mTIA6qs=">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</latexit> max g2C(Y) ⇢Z Y g(y)d (y) : 8y, g(y) 6 min x c(x, y) f(x) <latexit 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<latexit 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<latexit sha1_base64="ZGTgY0mCI1VHMWp5n15yAAny+Lk=">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</latexit> Proposition: The dual solution on g is equal ↵-a.e to fc. <latexit 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<latexit 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c-transforms: <latexit 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<latexit 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<latexit 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fc(y) def. = min x2X c(x, y) f(x) <latexit 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<latexit 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<latexit sha1_base64="KTePQAfBrlkXL99fiykWcKDj/c4=">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</latexit> gc(x) def. = min y2Y c(x, y) g(y) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  14. C-transforms Fixing f, solve the dual with respect to g:

    <latexit sha1_base64="izjhNSpYSgi9QeTHRhVJz7BqTyg=">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</latexit> <latexit sha1_base64="izjhNSpYSgi9QeTHRhVJz7BqTyg=">AABFp3ictVzvctu4EUeuf+6S/su1H/uFPSedpOPmbN912rmbzlxiO44vTuxEspNLlGQoiZKZ0KIiUrITnZ+jT9Ppt/YZ+gbtp75CdxcAAUogF3TTcGyDIH67iyWw2F2A6Y6TOMvX1v556aMf/PBHP/74k8tXfvLTn/38F1c//eVRlk4nveiwlybp5Gk3zKIkHkWHeZwn0dPxJApPukn0pPtmE58/mUWTLE5H7fzdOHpxEg5H8SDuhTlUvbq6fjc+i0fD4FpncG01yNJkFgX5cRT0p2ESnMb5cTCJsnHUy4M8hUbDa1+9urqydmuN/gXLhXVVWBHq30H66Wefi47oi1T0xFSciEiMRA7lRIQig+u5WBdrYgx1L8Qc6iZQiul5JM7FFcBOoVUELUKofQO/h3D3XNWO4B5pZoTuAZcEfiaADMR1wKTQbgJl5BbQ8ylRxtoq2nOiibK9g79dResEanNxDLUcTrf0xWFfcjEQf6I+xNCnMdVg73qKypS0gpIHVq9yoDCGOiz34fkEyj1Caj0HhMmo76jbkJ7/i1piLd73VNup+DdJeR2uQLRU79OCQihmRD+gtzmFZ1KeBDgPgUKk+oilU9L1CfV+BO3nUP8QrnMqaZ104ZpT7XktchMuF3KTRe7A5ULusMg9uFzIPRZ5AJcLeaCQiJ2Qzt34FlwufIvl/AguF/IRi3wMlwv5mEUeweVCHrHIZ3C5kM9Y5F24XMi7LPI+XC7kfRbZhsuFbLPIQ7hcyEMWuQ2XC7mtkNUzdQJXSnRiZlbehnKZB1qKBGpus/LdIevowt7xmNO9Ciw/q7fgrxu75aHTqAK77THuBhVYfuTtgI10Y3lbdI9WExf2HovdhRHgxu6y2G/F6wrstx4z7U0Flp9re9DOjeWt7wO4c2MfsNiHUHJj+TVqH2rc2H2PFWNcgT1gsY/E2wqsj9WfVGB5u98Cu+LG8utUG9q7sT7WdFqB5e3pEXgwbiy/Wj2BWjf2CYt9Ks4Ii2Xjo87JC0BLtkzzKdGsp/od2H0XVfTLpmTllul+50H3mXhf0VO9Ml+hdWdI8kcwz+uohWouV/cdW4yBS8hKlhRrVUK+dhfqQwYzLDBDwpywiJ0CseOJ2CsQe95yZYVdzsh/5rm0CkTLE9FVa13dCME2uYfu+8W6iaVEYepXaY3YWkDUeb84EnQ/Z+TJ6BoOmRerJJYiDwnTYq3AUqTGSr2V14j9EkLOiGOaL6sUmWG0hpqqo3Zc+BMSGdB9HeKUIkXdS82Dx+XKApVRZyyq60B1WdQ7B+odi5o6UFMWNXOgZizKWAUb1/EYAUb/+C7mdCdHgPTHq68APJDbsMLdg/kbwPg5AI/zMdXsw98WxfncVScZZg5wTcaMyouS/Z5AaS5WoN5EoFsUyyc0wyKQTLbcV/kEvJO2Qs45aaPPC68hKLIz/nRikmdY0EHPNKD51IzOfao5J09Slprh7xXzXpea4bdJ44jXpWb4XEmfX0D2tsK2L4BtwWwaK+2bclMaMtcjaejyFVqR0eLiWz1RYwbpnTWkv6vezO4F3ssmlaR+TLkZjczqX1bqXxMaRs+ZpedmVNDnkh62LgWNezJSMbYpN5UhpVV0pOQwd03fDLbpqzejy81oHIA3tknx/dwqNx2946I3ptyMxpGQOdZzihp0uRmNId1LfZhyMxqY2QlVTsGUm1p21ICM0025qVUfUcYZ801yzMsa4xVNyE+aKmox+Qf1mSE7IlhexzA/9FLoyKKekvFuq+l0i7WsXiLtL0Rg1fKGcqB/MbV8sDKNudhg/W8pQ15a35fpmDUeNb8HWgxg9sv9Bi4/jzGBzn+g9U6A4jobkZV7pnEbLA5HyWAB1VG1OestGr6viwjH1L2iWi5mM701euyQvc5o7I3JJ9wjzXJ62Kt8w1UUOQ3tlTTE02uiu/dqvpa1v8bixguIcTHSerT7JHft6mNYl9Zblo6vqx2lHC65v2TGL2a2B8raYMyTki1CWep42u10zsquw3V1VZh8unwW0BtFezUjqxHT7lfGRqE6My298TndG9qHtP+HPCSNHrzHQFEZC7lDhxl7zN0HZFFte8vxRn3pbKAsZ2R1tT2uRw8t9NCBbh7jbMKK8RBKbYgZDuGu7RHlXCl0lZLGJ+L3xU5sSm+wPqJPShZS05D2JipZyLoo+7hE5RTQOBpklO5PY5GOxneWKPFRv0seE7uWLf912iXWe+khjfHq0VydiekT1w3iGtCskTvI8m6Rg5Rg7nyyQf5rfS+RXxOOaEM5ri8tzlIvIzpdEFEEOybPOKHZxs2Ocms7P7X4RHM6EHqfHnfOU7KQAdm/ANanlMZkQD/2OQW9Wy8tQkI20sfuxIV34/J1YnaMGT8uFvIEhRlvEdmyKfHXdO3ZldFYlBGDXAfOF8a21ske+YIRcZ0o627mdv3qg0hzJsMeJZKiGSs3iP9N+q1/9DhZWRoRqGF8A5myda73kVLMgjoKaZWvt0G6rS3ltUKGl0pqs/4Zma6VJNuiiAvlwdW6D5x7dC954SiZkNzZUhu5jtZlc5HyeEGP2NsBRfHS7g/VCoxyr9IquUJzrkOjZAijIC+iCN2WyyIv8q3nVabuRzv7v1A3ui5rDSkGwmRwpYa43H9E0ZotZQKjWo7fNzSb3FqfLLSq5zOisXhizeXvofY38FvLre/96HRLVuEOjQFJwdwZjciaYKmFH687JV56ZGpa5t7wM2NSt7JrLhJfS+tmYuxZYyoHNGrOVNZCly9C47VF47WnDtu0r2m0qOu1JXrFxhZttTPqy68Jt3YDylOWMu+RaVTsIaUdS/lR7bNU+Rhfo96ztNZYWiHMVns3wJ7zPkj3XF+c3d8Xq3sg7pJv0yMPTMYvfZqlMflcurY+UpMUkPOXyr7as79DNci9SxYUKcszozhj5K5Tj67zQtLfqpUtJTtvLII+I3Wq2mgb26HyF0vIE5oTGc1LjfiSWkRKfluOYMEi3bJ8joAy/yH5VNLvqI+Z7dbmnQQlf8LEm3JWGV4yUhiR/rnM2+5S9Lprxa8BxYRT5V13gVbzN4wUJEZnEtyeZUZvCFc5uZMgPdou2c9lOyV38UaWRLdI6rn4s4eNkVGvGev22NI91n37HbRErZu37mrB80u8OXL8LrKjF9KqdqJ81PnC/cVohWqVK9/X6WG6wNfoY0pt7MjCRHllTEd87c1FStSMi8T4cGnWiybyN5O8icxyd8qXsm6tKZczDdLGHFO8xJ05RYTLu7vh9OZuMv3oLtHrEtamJms4SpiNS1V+wLa0mJW6vLQOydrLtatRYq1EVSuFpm6vFsZ+SwsZkfVLBJezka1t2TulKIXPwkgKPSFPD1fFhzbNr8VX9DsQruhQc/TJHbbAv70tNsX2BzgN8VaVZUYzoBq0Bf2F2DtU/Sy3qNfRW4u6Td+Hgz+PGHTNSR/TStpUdkmZl9ym7k//lKzARESs9KZl8z7YXPieLHNq0p+YLBvfm1jo736a9kVz8OlJmYs/H7mvwfViIPT3U836oKnzPShzaMJDn2Pwe+emdXNeNqd6fS1z8eUhVwG946JxuPNXHauYdj4WamK9kQ/PAa3DoIa6Xi3+135oPoZTc16+3DL6ru21x1uX7SKVkUV/uPmcMdx8RnM1R3+eadE74y25+Um/L2j0plKrNx+ePvqjZgxoXnMh86C8dBJvjyIjry8V3BdwyZCK/4i/XeK/fHhb0KiSowklvU9RTU234KnprztdvdPPfGQydKpkKlMzcUSLTsRuil1xF342Cw+w6elQ+d2m/ItY97e6fagdkPXQWXSZOehQXUTZD7OL1qd7c362SmI8yyvP9rahBvfC96gWz/k+pPZ41rdd6lv11ypyrj8QqeiXIpLF3T0zr7rQg/LOm8wB6W+KAzpLL7NY8uTZicfeojw/JSMk1xcci5LORShM3qWOctdJ2f4+YZl21+pbfTaxTmp9crt+RA8Z+ebUwmi6R/NtrM4b4O4HfiUQFjmuQHxOdaFaq9Bv4HR04JDhOeUnujQa1iBe/INYhb+rquzW28GSpBmNiLJEZ9az+vNo585Rar7fvE7ZOJ0vnKl2KeUWzB5m/RvcquQi3149fliDH1pStuhtvaHofyLqM5jTGppTJZO9qzwSOvsq9YCxdViMj/poflbDa+bR//uV6PuWpDsgS5dy/gHtKk6IXqJ0s03Sy9Od9dnjezXS6u9UJU1zvtOMA31Ss35nIlHjrtoWydOYXMYoqqCz+GUUv8vCy8NL4yMLR2XKSjL1+Dp65iHLzIPOgJFmwFIYspKoGfzq6sr64v8/slw42ri1vnZr/dHGyjd31P9N8on4tfhM3IC18o/iGxihB+IQOP1F/FX8Xfxj++b2/vbR9lPZ9KNLCvMrUfq3Hf4X7utxqQ==</latexit> <latexit 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<latexit sha1_base64="izjhNSpYSgi9QeTHRhVJz7BqTyg=">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</latexit> max g2C(Y) ⇢Z Y g(y)d (y) : 8(x, y), f(x) + g(y) 6 c(x, y) <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="Ctw3wt9QBMWIGiay2Uv+mTIA6qs=">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</latexit> max g2C(Y) ⇢Z Y g(y)d (y) : 8y, g(y) 6 min x c(x, y) f(x) <latexit 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<latexit 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<latexit sha1_base64="ZGTgY0mCI1VHMWp5n15yAAny+Lk=">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</latexit> Proposition: The dual solution on g is equal ↵-a.e to fc. <latexit 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<latexit 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sha1_base64="yF4j1feOPivb9/Uc6cOlb/luwYo=">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</latexit> Cost c(x, y) = hx, yi: <latexit 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<latexit 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<latexit 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R ||x y||2d⇡(x, y) = 2 R hx, yid⇡(x, y) + R ||x||2d↵(x) + R ||y||2d (y) <latexit 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<latexit 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constant <latexit 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<latexit 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<latexit 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fc = ( f)⇤ where h⇤(y) def. = sup x hx, yi f(x) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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c-transforms: <latexit 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<latexit 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<latexit 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fc(y) def. = min x2X c(x, y) f(x) <latexit 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<latexit 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<latexit sha1_base64="KTePQAfBrlkXL99fiykWcKDj/c4=">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</latexit> gc(x) def. = min y2Y c(x, y) g(y) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  15. Application: existence of dual solutions Proposition: if is -Lipschitz, then

    is -Liphschitz. c L fc L supf,g {∫ fdα + ∫ gdβ : f ⊕ g ≤ c, f, g ∈ 𝒞 } supf,g {∫ fdα + ∫ gdβ : f ⊕ g ≤ c, f, g ∈ LipL} replace by f gc replace by g fc Proposition (Ascoli-Arzelà)): if is compact is compact. 𝒳 {f ∈ LipL ( 𝒳 ), f(0) = 0} Corrolary : if is Lipschitz, dual solutions exists. c
  16. Alternate Minimization and W1 (f, g) 7 ! (f, fc)

    <latexit 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  17. Alternate Minimization and W1 (f, g) 7 ! (f, fc)

    <latexit 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<latexit 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7 ! (fcc, fc) 7 ! (fcc, fccc) <latexit 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<latexit 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  18. Alternate Minimization and W1 (f, g) 7 ! (f, fc)

    <latexit 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<latexit 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7 ! (fcc, fc) 7 ! (fcc, fccc) <latexit 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<latexit 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= (fcc, fc) <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="5f50aKJRcgV4L/4RPQpP5LnOUlY=">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</latexit> Proposition: fccc = fc. <latexit 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<latexit 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  19. Alternate Minimization and W1 W1 case: c(x, y) = d(x,

    y) <latexit 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<latexit 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<latexit sha1_base64="3pLz5EsNOhKHqOGj1+2u5vKJpHg=">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</latexit> Proposition: <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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9f s.t. g = fc () g is 1-Lipschitz. <latexit 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<latexit 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<latexit sha1_base64="c75+5GfYei81PRvPg7r39TJHnEs=">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</latexit> fcc = fc <latexit 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<latexit 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<latexit 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(f, g) 7 ! (f, fc) <latexit 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<latexit 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7 ! (fcc, fc) 7 ! (fcc, fccc) <latexit 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<latexit 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= (fcc, fc) <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="5f50aKJRcgV4L/4RPQpP5LnOUlY=">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</latexit> Proposition: fccc = fc. <latexit 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<latexit 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  20. Alternate Minimization and W1 W1 case: c(x, y) = d(x,

    y) <latexit 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<latexit 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<latexit sha1_base64="3pLz5EsNOhKHqOGj1+2u5vKJpHg=">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</latexit> Proposition: <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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9f s.t. g = fc () g is 1-Lipschitz. <latexit 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<latexit 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<latexit sha1_base64="c75+5GfYei81PRvPg7r39TJHnEs=">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</latexit> fcc = fc <latexit 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<latexit 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<latexit sha1_base64="mY32wCfwVAJhi6zl4+SGhjoLqv4=">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</latexit> W1(↵, ) = max f,g {hf, ↵i + hg, i : f g 6 c} <latexit 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<latexit 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<latexit sha1_base64="0sTxDRr6szhd/uQj/2Nsw8M7qCc=">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</latexit> = max f hf, ↵i + hfc, i <latexit 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<latexit 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(f, g) 7 ! (f, fc) <latexit 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<latexit 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7 ! (fcc, fc) 7 ! (fcc, fccc) <latexit 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<latexit 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= (fcc, fc) <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="5f50aKJRcgV4L/4RPQpP5LnOUlY=">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</latexit> Proposition: fccc = fc. <latexit 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<latexit 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  21. Alternate Minimization and W1 W1 case: c(x, y) = d(x,

    y) <latexit 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<latexit 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<latexit sha1_base64="3pLz5EsNOhKHqOGj1+2u5vKJpHg=">AABFmnictVzbchu5EYU3t7Vz8yaPycNkJafslKKVlE0ltVtbtdbFslayLZuU7LVpq4bkiKZNcWjeLJurH8jX5DV5yXfkD5Kn/EL6AgwwJGYaoziakogBcbobPUCju4FRc9DrjsZra/+88tH3vv+DH/7o46vXfvyTn/7s59c/+cXxKJ0MW8lRK+2lwyfNeJT0uv3kaNwd95Ing2ESnzV7yePm6y38/vE0GY66ab8+fjdInp/FnX73tNuKx1B1cn15+fHJ+nJjnJwDeBa1gNQXF9Fy6+b5yrtbX7XpY/nk+tLa6hr9RIuFdV1YUvrnMP3k089UQ7VVqlpqos5UovpqDOWeitUIrmdqXa2pAdQ9VzOoG0KpS98n6kJdA+wEWiXQIoba1/C3A3fPdG0f7pHmiNAt4NKD3yEgI3UDMCm0G0IZuUX0/YQoY20R7RnRRNnewWdT0zqD2rF6CbUSzrQMxWFfxupU/Zn60IU+DagGe9fSVCakFZQ8cno1BgoDqMNyG74fQrlFSKPniDAj6jvqNqbv/0UtsRbvW7rtRP2bpLwBV6RquvdpRiFWU6If0dOcwHcsTw84d4BCovuIpbek6zPqfR/az6D+PlwXVDI6acI1o9qLUuQWXD7klojchcuH3BWRB3D5kAci8hAuH/JQIxE7JJ378TW4fPiayPkhXD7kQxH5CC4f8pGIPIbLhzwWkU/h8iGfisg7cPmQd0TkPlw+5L6IrMPlQ9ZF5BFcPuSRiNyBy4fc0cjimTqEKyU6XWFW3oZyngdaih7U3Bbl2yTr6MNuBszpVgFWntXb8OnHbgfoNCnA7gSMu9MCrDzydsFG+rGyLbpLq4kPe1fE7sEI8GP3ROw36lUB9puAmfa6ACvPtQNo58fK1vce3Pmx90TsfSj5sfIa9QBq/NgHASvGoAB7KGIfqjcF2BCrPyzAyna/BnbFj5XXqTq092NDrOmkACvb02PwYPxYebV6DLV+7GMR+0SdExbL1kedkReAlmyR5hOiWU71W7D7Pqrol03Iyi3S/TaA7lP1vqCnZmW+RutOh+RPYJ6XUYv1XC7uO7YYAJdYlKyXrVU98rWbUB8LmE6G6RDmTETsZojdQMRBhjgIlmuU2eUR+c8yl1qGqAUimnqtKxsh2GYcoPt2tm5iqacx5au0QWzPIcq8XxwJpp9T8mRMjYQcZ6sklpIACdNsrcBSosdKuZU3iAc5BM+IlzRfVigyw2gNNVVG7WXmTzAyovsyxFuKFE0vDQ8ZN9YWKI86F1FND6opot55UO9E1MSDmoioqQc1FVHWKri4RsAIsPrHZzGjOx4B7I8XXxF4ILdhhbsL8zeC8XMIHucjqnkAnzWK86WrTDLMHOCajBmV5zn7PYTSTC1BvY1AtymW79EMS0AybvlA5xPwjm0Fzzm20ReZ1xBl2ZlwOl2Sp5PRQc80ovlUjc4+1VyQJ8mlavi72bw3pWr4HdI44k2pGn6spR9fQva6xtYvga3BbBpo7dtyVRqc62EapnyNVmS0uPhUz/SYQXrnFenv6Sezd4nnskUl1o8tV6Mxcvo3yvWvCg2r55Gj52pU0OdiD9uUoso96esY25arypDSKtrXcti7qk8G27T1kzHlajQOwRvbovh+5pSrjt5B1htbrkbjWHGO9YKiBlOuRqND96wPW65GAzM7sc4p2HJVy44a4Djdlqta9T5lnDHfxGOea6xXNCQ/aaKpdck/KM8MuRHB4jqG+aEXykQW5ZSsd1tMp5mtZeUSGX8hAas2rigH+hcTxwfL05ipDdH/ZhnGufV9kY5d41HzB6DFCGY/7zdI+XmMCUz+A613DyiuixFZvmcGtyHicJSczqEaunYseouW76sswrF1J1QrxWy2t1aPDbLXIxp7A/IJD0izkh4OCp9wEUVJQwc5Dcn0qujuvZ6vee2vibjBHGKQjbQW7T7xrl15DOvTes3R8Q29ozSGi/eX7PjFzPaptjYY86Rki1CWMp5uO5OzcutwXV1RNp/O30X0RNFeTclqdGn3ayRGoSYzzd74jO4t7SPa/0MeTKMFzzHSVAaKd+gwY4+5+4gsqmtvJd6oL5MN5PKIrK6xx+XojoPueNDVY5wtWDHuQ6kOMcMR3NUDopxrma5S0vhQ/T7biU3pCZZH9L2chTQ02N4kOQtZFmW/zFF5C2gcDRylh9OYp2PwjQVKctTvk8fGrnnLf4N2ic1eekxjvHg0F2di2sR1g7hGNGt4B5nv5jmwBDPvNxvkv5b3EvlV4Yg2VOL6wuHMeunT6YKEItgBecY9mm3S7Mi3dvNT898YTofK7NPjznlKFjIi+xfB+pTSmIzo1z2nYHbr2SL0yEaG2J1u5t34fJ2uOMasH9dVfILCjreEbNmE+Bu67uwa0VjkiIHXgYu5sW10ckC+YEJch9q627ldvvog0p7JcEcJU7Rj5Sbxv0V/za8ZJ0sLIwI1jE9gpG2d73mkFLOgjmJa5cttkGnrSrmcyfBCS23XPyvTck6ybYq4UB5crdvAuUX3zAtHyZDkHi204XW0LJuLlAdzesTenlIUz3a/o1dglHuFVsklmnMNGiUdGAXjLIowbaUs8jzfcl556mG0R/8X6lbXea0hxUjZDC5rSMr9JxStuVL2YFTz+H1Ns8mv9eFcq3I+fRqLZ85c/g5qfwN/jdzmPoxOM2cVNmkMMAV7ZzXCNdFCizBemzleZmQaWvbe8rNj0rRyay4TX7N1szH2tDKVQxo15zprYcqXofHKofEqUId12te0WjT1xhKdiLFFXe+MhvKrwq1egfJEpCx7ZAbVDZDSjaXCqLZFqnKMb1DvRVprIq0YZqu7G+DO+RCkf67Pz+7vstU9UnfIt2mRB8bxS5tmaZd8LlNbHqkxBeT8ubav7uxvUA1yb5IFRcp8ZhRnDO86tei6yCT9rV7ZUrLz1iKYM1JvdRtjYxtU/sMC8ozmxIjmpUF8Ti0SLb8rRzRnkVYdnyOizH9MPhX7HeUxs9vaPpMo50/YeJNnleXFkUKf9C9l3vYWotc9J36NKCacaO+6CbSqP2GkwBiTSfB7liN6QrjK8U4Ce7RNsp+Ldop38fqORKsk9Ux9FWBjOOq1Y90dW6bHpm+/g5aodfvUfS1kfr1gjhK/y+zoxbSqnWkfdTZ3fzlasV7l8vdlepjM8bX6mFAbN7KwUV4e01BfBnNhiapxYUwIl2q9qCJ/NcmryMy7U6GUTWtDOZ9pYBvzkuIl6cwpInze3U2vN3dL6EdzgV6TsC41rpEoYTYu1fkB19JiVurqwjrEtVdLV6OesxIVrRSGurtaWPvNFjIh69dTUs6GW7uyN3JRipyFYQotxaeHi+JDl+aX6gv6GylfdGg4huQOa+Df3lZbaucDnIZ4o8uc0YyoBm1Bey72jnU/8y3KdfTGoe7SD+EQzqMLupak79JKWlV2pixL7lIPp/+WrMBQJaL0tmX1Prhc5J4scqrSny5ZNrk3XWXe+6naF8MhpCd5LuF8eF9D6sWpMu9PVeuDoS73IM+hCg9zjiHsmdvW1Xm5nMr1tcgllAevAmbHxeBw5684VrHtQizU0HkiH54DWofTEupmtfhf+2H4WE7VeYVyG9F7ba8Cnjq3S3RGFv3h6nPGcgsZzcUcw3mmWe+st+Tnx35fVOlJpU5vPjx99EftGDC8ZorzoLJ0jHdHkZU3lAruC/hkSNV/1D+uyG8+vMloFMlRhZLZpyimZlrI1Mzbnb7eme9CZLJ0imTKU7NxRI1OxG6pPXUHfrcyD7Dq6VB+b5M/Eet/V7cNtadkPUwWnTMHDapLKPthd9HadG/PzxZJjGd5+WxvHWpwL/yAavGc731qj2d967m+Fb+twnP9nkpVOxeRzO/u2XnVhB7kd944B2TeKY7oLD1nsfjk2VnA3iKfn+IIyfcGx7ykMxUrm3cpo9z0UnbfT1ik3XT6Vp5NLJPanNwuH9EdQb4ZtbCabtF8G+jzBrj7gW8JxFmOK1KfUV2s1yr0GyQdHXpkeEb5iSaNhjWIF/+oVuBzRZf9ejtckHREIyIv0bnzXfl5tAvvKLXvb96gbJzJF051u5RyC3YPs/wJbhdy4adXju+U4DuOlDV6Wq8p+h+q8gzmpITmRMvk7ir3lcm+sh4wto6z8VEezU9LeE0D+r9fiN53JN0FWZqU849oV3FI9HpaNzskPZ/uLM8e3y2R1rynyjTt+U47DsxJzfKdiZ4ed8W2iE9jShmjpIDO/JtR8i6LLI8sTYgsEpWJKMkk4O3oaYAs0wA6p4I0pyKFjiiJnsEn15fW5///yGLheGN1fW11/eHG0teb+n+TfKx+pT5VN2Gt/JP6GkbooToCTn9Rf1V/U3/f+fXO5s7ezj43/eiKxvxS5X526v8FRLZsBQ==</latexit> Proposition: <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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9f s.t. g = fc () g is 1-Lipschitz. <latexit 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<latexit 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<latexit sha1_base64="c75+5GfYei81PRvPg7r39TJHnEs=">AABFyHictVxfc9u4EUeu/y7uv1z72Bf27HRynZzPdq/TTm9u5hLbcZwoiRPJSS5RkqEkSmZCiwop2U50fumn6ls/R1/62utTv0J3FwABSiAXdNNwbIMgfruLJbDYXYDpTZI4n25s/OPSRz/44Y9+/JOPL6/89Gc//8Uvr3zyq8d5Osv60WE/TdLsaS/MoyQeR4fTeJpETydZFB73kuhJ7802Pn9yEmV5nI4703eT6MVxOBrHw7gfTqHq1ZVHa93oDNjkQXe4FuTr0/VgrTsKvobbl/1gpft2Fg66rXQ8SqLhNItHR9Mwy9LTgB6sdEdrQZwHm5+34kneP4qn79dXVl5dWd1Y36B/wXJhUxVWhfp3kH7y6ReiKwYiFX0xE8ciEmMxhXIiQpHD9Vxsig0xgboXYg51GZRieh6Jc7EC2Bm0iqBFCLVv4PcI7p6r2jHcI82c0H3gksBPBshAXAVMCu0yKCO3gJ7PiDLWVtGeE02U7R387Slax1A7FUdQy+F0S18c9mUqhuLP1IcY+jShGuxdX1GZkVZQ8sDq1RQoTKAOywN4nkG5T0it54AwOfUddRvS8++pJdbifV+1nYl/k5RX4QpEW/U+LSiE4oToB/Q2Z/BMypMA5xFQiFQfsXRKuj6m3o+h/Rzq78N1TiWtkx5cc6o9r0Vuw+VCbrPIPbhcyD0W2YLLhWyxyAO4XMgDhURsRjp349twufBtlvNDuFzIhyzyEVwu5CMW+RguF/Ixi3wGlwv5jEXegsuFvMUi78LlQt5lkR24XMgOizyEy4U8ZJG7cLmQuwpZPVMzuFKiEzOz8gaUyzzQUiRQc4OV7yZZRxf2psec7ldg+Vm9A3/d2B0PnUYV2F2PcTeswPIjbw9spBvL26LbtJq4sLdZ7D6MADd2n8XeEa8rsHc8ZtqbCiw/11rQzo3lre89uHNj77HY+1ByY/k16gHUuLEPPFaMSQX2gMU+FG8rsD5WP6vA8na/DXbFjeXXqQ60d2N9rOmsAsvb08fgwbix/Gr1BGrd2Ccs9qk4IyyWjY86Jy8ALdkyzadEs57qt2D3XVTRL5uRlVum+60H3WfifUVP9cq8QuvOiOSPYJ7XUQvVXK7uO7aYAJeQlSwp1qqEfO0e1IcMZlRgRoQ5ZhF7BWLPE9EqEC1vufLCLufkP/Nc2gWi7YnoqbWuboRgm6mH7gfFuomlRGHqV2mN2FlA1Hm/OBJ0P0/Ik9E1HHJarJJYijwkTIu1AkuRGiv1Vl4jHpQQckYc0Xy5TpEZRmuoqTpqR4U/IZEB3dchTilS1L3UPHjcVFmgMuqMRfUcqB6LeudAvWNRMwdqxqJOHKgTFmWsgo3reowAo398F3O6kyNA+uPVVwAeyA1Y4W7D/A1g/ByAx/mIah7A3zbF+dxVJxlmDnBNxozKi5L9zqA0F6tQbyLQHYrlE5phEUgmWz5Q+QS8k7ZCzjlpo88LryEosjP+dGKSZ1TQQc80oPnUjM5dqjknT1KWmuFvF/Nel5rhd0njiNelZvipkn56Adk7Ctu5ALYNs2mitG/KTWnIXI+kocsrtCKjxcW3eqzGDNI7a0h/X72Z/Qu8l20qSf2YcjMaudW/vNS/JjSMnnNLz82ooM8lPWxdChr3ZKxibFNuKkNKq+hYyWHumr4ZbDNQb0aXm9E4AG9sm+L7uVVuOnonRW9MuRmNx0LmWM8patDlZjRGdC/1YcrNaGBmJ1Q5BVNuatlRAzJON+WmVn1MGWfMN8kxL2uMV5SRnzRT1GLyD+ozQ3ZEsLyOYX7opdCRRT0l491W0+kVa1m9RNpfiMCqTRvKgf7FzPLByjTmYov1v6UM09L6vkzHrPGo+RZoMYDZL/cbuPw8xgQ6/4HWOwGKm2xEVu6Zxm2xOBwlwwVUV9VOWW/R8H1dRDim7hXVcjGb6a3RY5fsdU5jb0I+YYs0y+mhVfmGqyhyGmqVNMTTa6K792q+lrW/weImC4hJMdL6tPskd+3qY1iX1tuWjq+qHaUpXHJ/yYxfzGwPlbXBmCclW4Sy1PG02+mclV2H6+p1YfLp8llAbxTt1QlZjZh2v3I2CtWZaemNz+ne0D6k/T/kIWn04T0GispEyB06zNhj7j4gi2rbW4436ktnA2U5J6ur7XE9emShRw508xhnG1aM+1DqQMxwCHcdjyhnpdBVShrPxOfFTmxKb7A+ok9KFlLTkPYmKlnIuij7qETlFNA4GmSU7k9jkY7Gd5co8VG/Sx4Tu5Yt/1XaJdZ76SGN8erRXJ2JGRDXLeIa0KyRO8jybpGDlGDufLJF/mt9L5FfE45oQzmuLy3OUi9jOl0QUQQ7Ic84odnGzY5yazs/tfhEczoQep8ed85TspAB2b8A1qeUxmRAP/Y5Bb1bLy1CQjbSx+7EhXfj8nVidowZPy4W8gSFGW8R2bIZ8dd07dmV01iUEYNcB84XxrbWSYt8wYi4Zsq6m7ldv/og0pzJsEeJpGjGyjXi/xn91j96nKwujQjUML6BXNk61/tIKWZBHYW0ytfbIN3WlnKtkOGlktqsf0amtZJkOxRxoTy4Wg+Ac5/uJS8cJRnJnS+1ketoXTYXKU8W9Ii9HVIUL+3+SK3AKPd1WiVXac51aZSMYBRMiyhCt+WyyIt863mVqfvRzv8v1I2uy1pDioEwGVypIS73H1G0ZkuZwKiW4/cNzSa31rOFVvV8xjQWj625/B3U/hZ+a7n1vR+dXskq3KQxICmYO6MRWRMstfDjdbPES49MTcvcG35mTOpWds1F4mtp3UyMfdKYygGNmjOVtdDli9B4bdF47anDDu1rGi3qem2JXrGxRUftjPrya8Kt04DyjKXMe2QaFXtIacdSflQHLFU+xteo9yytDZZWCLPV3g2w57wP0j3XF2f3d8XqHohb5Nv0yQOT8cuAZmlMPpeurY/UJAXk/KWyr/bs71INcu+RBUXK8swozhi569Sn67yQ9HdqZUvJzhuLoM9Inao22sZ2qfyHJeQxzYmc5qVGfEktIiW/LUewYJHWLZ8joMx/SD6V9DvqY2a7tXknQcmfMPGmnFWGl4wUxqR/LvO2vxS97lvxa0Ax4Ux51z2g1fwNIwWJ0ZkEt2eZ0xvCVU7uJEiPtkf2c9lOyV28sSXROkk9F1972BgZ9Zqxbo8t3WPdt99DS9S6eeuuFjy/xJsjx+8iO3ohrWrHykedL9xfjFaoVrnyfZ0eZgt8jT5m1MaOLEyUV8Z0xVfeXKREzbhIjA+XZr1oIn8zyZvILHenfCnr1ppyOdMgbcwRxUvcmVNEuLy7a05v7jOmH70lej3C2tRkDUcJs3Gpyg/YlhazUpeX1iFZe7l2NUqslahqpdDU7dXC2G9pISOyfongcjaytS17txSl8FkYSaEv5OnhqvjQpvmV+Av9DoQrOtQcfXKHbfBvb4htsfsBTkO8VWWZ0QyoBm3BYCH2DlU/yy3qdfTWom7T9+HgzyMGXXPSx7SSNpVdUuYlt6n70z8lK5CJiJXetGzeB5sL35NlTk36E5Nl43sTC/3dT9O+aA4+PSlz8ecj9zW4XgyF/n6qWR80db4HZQ5NeOhzDH7v3LRuzsvmVK+vZS6+POQqoHdcNA53/qpjFdPOx0Jl1hv58BzQOgxrqOvV4n/th+ZjODXn5cstp+/aXnu8ddkuUhlZ9IebzxnDzWc0V3P055kWvTPekpuf9PuCRm8qtXrz4emjP2rGgOY1FzIPyksn8fYoMvL6UsF9AZcMqfiP+Psl/suHtwWNKjmaUNL7FNXUdAuemv6609U7/cxHJkOnSqYyNRNHtOlE7LbYF7fgZ7vwAJueDpXfbcq/iHV/qzuA2iFZD51Fl5mDLtVFlP0wu2gDujfnZ6skxrO88mxvB2pwL7xFtXjO9z61x7O+nVLfqr9WkXP9nkjFoBSRLO7umXnVgx6Ud95kDkh/UxzQWXqZxZInz4499hbl+SkZIbm+4FiUdC5CYfIudZR7Tsr29wnLtHtW3+qziXVS65Pb9SN6xMg3pxZG032abxN13gB3P/ArgbDIcQXiC6oL1VqFfgOnowOHDM8pP9Gj0bAB8eIfxXX4e12V3Xo7WJI0pxFRlujMelZ/Hu3cOUrN95tXKRun84Unql1KuQWzh1n/Bncquci3V48f1eBHlpRteltvKPrPRH0Gc1ZDc6ZksneVx0JnX6UeMLYOi/FRH82f1PA68ej/3Ur0XUvSPZClRzn/gHYVM6KXKN3skvTydGd99vh2jbT6O1VJ05zvNONAn9Ss35lI1LirtkXyNCaXMYoq6Cx+GcXvsvDy8NL4yMJRmbGSzDy+jj7xkOXEg86QkWbIUhixkqgZ/OrK6ubi/z+yXHi8tb65sb75cGv1m5vq/yb5WPxGfCquwVr5J/ENjNADcQic/ib+Kf4lvt+9szvZPd19J5t+dElhfi1K/3b/+l/nAn2d</latexit> fcc = fc <latexit 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<latexit 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<latexit sha1_base64="mY32wCfwVAJhi6zl4+SGhjoLqv4=">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</latexit> W1(↵, ) = max f,g {hf, ↵i + hg, i : f g 6 c} <latexit 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<latexit 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<latexit 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  22. Alternate Minimization and W1 W1 case: c(x, y) = d(x,

    y) <latexit 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<latexit 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<latexit 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<latexit sha1_base64="3pLz5EsNOhKHqOGj1+2u5vKJpHg=">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</latexit> Proposition: <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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9f s.t. g = fc () g is 1-Lipschitz. <latexit 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<latexit 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<latexit sha1_base64="c75+5GfYei81PRvPg7r39TJHnEs=">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</latexit> fcc = fc <latexit 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<latexit 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<latexit sha1_base64="mY32wCfwVAJhi6zl4+SGhjoLqv4=">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</latexit> W1(↵, ) = max f,g {hf, ↵i + hg, i : f g 6 c} <latexit 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<latexit 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<latexit sha1_base64="0sTxDRr6szhd/uQj/2Nsw8M7qCc=">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</latexit> = max f hf, ↵i + hfc, i <latexit 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<latexit 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sha1_base64="ic+EJJkilNva+gXX7zKFsb+pVEk=">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</latexit> = max f hfc, ↵i <latexit 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<latexit 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<latexit sha1_base64="UlA+HDcgwd1cLazasVHhkEBuJNw=">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</latexit> = max Lip(f)61 hf, ↵ i = ||↵ ||W1 <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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(f, g) 7 ! (f, fc) <latexit 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<latexit 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7 ! (fcc, fc) 7 ! (fcc, fccc) <latexit 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<latexit 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= (fcc, fc) <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="5f50aKJRcgV4L/4RPQpP5LnOUlY=">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</latexit> Proposition: fccc = fc. <latexit 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<latexit 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  23. Euclidean and Graphs W1 Case d(x, y) = ||x y||:

    <latexit 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<latexit 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||↵ ||W1 = max ||rf(x)||1 61 hf, ↵ i = min div(u)=↵ Z ||u(x)||dx <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  24. Euclidean and Graphs W1 Case d(x, y) = ||x y||:

    <latexit 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<latexit 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f f <latexit 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<latexit 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<latexit 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zero <latexit 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<latexit 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<latexit 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<latexit 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On graph: d(x, y) = Geodw(x, y) <latexit 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<latexit 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||a b||W1 = max |ri,j f|61 hf, a bi = min div(u)=a b P i,j wi,j |ui,j | <latexit 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sha1_base64="gjD87KdevcxjdWiIBEx1DQ5Xpvc=">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</latexit> ri,jf def. = w 1 i,j (fi fj) <latexit 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<latexit 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<latexit 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||↵ ||W1 = max ||rf(x)||1 61 hf, ↵ i = min div(u)=↵ Z ||u(x)||dx <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  25. W1 On Surfaces [Solomon, Rustamov, Guibas, Butscher, SIGGRAPH 2014] <latexit

    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<latexit 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<latexit 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<latexit 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  26. W1 On Sub-domains [Solomon, Rustamov, Guibas, Butscher, SIGGRAPH 2014] <latexit

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<latexit 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<latexit 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<latexit 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<latexit 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  27. Dual Norms B = {f : ||f||1 6 1} <latexit

    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<latexit 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<latexit 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B = {f : ||rf||1 + ||f||1 6 1} <latexit 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<latexit 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B = f : ||r(k)f||2 6 1 <latexit 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B = {f : ||rf||1 6 1} <latexit 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Total variation <latexit 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Flat norm (unbalanced) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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Sobolev ˙ H k <latexit 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B = {neural networks} <latexit 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<latexit 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<latexit 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?? (Non-convex) <latexit sha1_base64="R9OfLxXBa5Yo+C9fQpttxAGpwpI=">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</latexit> <latexit 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<latexit 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<latexit 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(k > d 2 ) <latexit 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<latexit 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<latexit sha1_base64="Ms4Qrm3ttoipo3NT/fT+AQSs9s8=">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</latexit> ||↵ ||B def. = sup f2B R f(x)d(↵ )(x) <latexit 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<latexit 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  28. Dual Norms B = {f : ||f||1 6 1} <latexit

    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<latexit 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<latexit 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B = {f : ||rf||1 + ||f||1 6 1} <latexit 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<latexit 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B = f : ||r(k)f||2 6 1 <latexit 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B = {f : ||rf||1 6 1} <latexit 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Total variation <latexit 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<latexit 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(k > d 2 ) <latexit 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<latexit 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<latexit sha1_base64="Ms4Qrm3ttoipo3NT/fT+AQSs9s8=">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</latexit> ||↵ ||B def. = sup f2B R f(x)d(↵ )(x) <latexit 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<latexit 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sha1_base64="O57Axf1tuA1vyT6SVOjsc611Lds=">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</latexit> Proposition: <latexit 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<latexit 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<latexit 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If C(X) ⇢ Span(B), then || · ||B is stronger than weak convergence. <latexit 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<latexit 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If B ⇢ C(X) is compact, then || · ||B is weaker than weak convergence. <latexit 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<latexit 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<latexit 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|| · ||B metrizes weak convergence. <latexit 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<latexit 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  29. Wasserstein GANs ⇣ g✓ ↵✓ <latexit 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<latexit 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<latexit

    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<latexit 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<latexit 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Generative model fitting: <latexit 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<latexit 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min ✓ ||↵✓ ||B <latexit 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<latexit 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<latexit 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<latexit 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g✓ <latexit 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<latexit 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<latexit 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<latexit sha1_base64="w7N6FQ/LhOKDydfLs6nSQv+DBsw=">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</latexit>
  30. Wasserstein GANs ⇣ g✓ ↵✓ <latexit 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<latexit 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<latexit

    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<latexit 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<latexit 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Generative model fitting: <latexit 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<latexit 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min ✓ ||↵✓ ||B <latexit 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<latexit 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<latexit 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<latexit 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g✓ <latexit 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<latexit 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<latexit 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<latexit 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= min ✓ sup f2B R fd↵✓ 1 m P j f(yj) <latexit 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<latexit 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  31. Wasserstein GANs ⇣ g✓ ↵✓ <latexit 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<latexit 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<latexit

    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<latexit 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<latexit 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Generative model fitting: <latexit 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<latexit 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min ✓ ||↵✓ ||B <latexit 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<latexit 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<latexit 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<latexit 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g✓ <latexit 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<latexit 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p/tkpifJeXv9vbhRY8C29RK77n+4D647u+3dLYqr9Bwtf6fZawQSkiWT7dU+sqgBGUT954Dkh+z9ejd+l5Fou/eTZ2OFuU708tSzSnO/Y3C4JKfKBJ2ae5OhVn9XhygG/Y+0V+yGOfUZsv7DzuuTbO7UrO7SXOGWmnzOGNdq/+3awqLnsal0GRO7sQ/RKKs9V5Xn1udL+SC38HvR4/qsGPNCk7pP2XFAmnrD6bl9fQzIVM+gnrhMlMJNcDxpl+8bzrI9uLGl4XDuO/V4m+p0l6CLIElP/26IQtJXqx0M0BSc/fdKzPpN6tkVZ8j/L02vrW8v8yWK2cbG9sbW5sPdpe/3pX/J+Dj9hv2CfsJqzxP7KvgVqbHQOHf639eu2TtfWdv+78e+c/susHa6LyK1b62b3yX+ao0p4=</latexit>
  32. Wasserstein GANs ⇣ g✓ ↵✓ <latexit 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<latexit 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<latexit

    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<latexit 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<latexit 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Generative model fitting: <latexit 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<latexit 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min ✓ ||↵✓ ||B <latexit 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<latexit 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<latexit 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<latexit 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g✓ <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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= min ✓ sup f2B R fd↵✓ 1 m P j f(yj) <latexit 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<latexit 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= min ✓ sup f2B R f(g✓(z))d⇣ 1 m P j f(yj) <latexit 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{f⇠ }⇠ ⇢ B <latexit 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<latexit 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<latexit 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min ✓ sup ⇠ R f⇠(g✓(z))d⇣ P j f⇠(yj) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  33. Wasserstein GANs ⇣ g✓ ↵✓ <latexit 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<latexit 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<latexit

    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<latexit 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<latexit 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Generative model fitting: <latexit 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<latexit 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min ✓ ||↵✓ ||B <latexit 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<latexit 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<latexit 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<latexit 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g✓ <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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Weight clipping ||⇠||1 6 1. <latexit 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<latexit 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<latexit 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<latexit 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Wasserstein GANs, <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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[Arjovsky, Chintala,Bottou, 2017]: <latexit 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<latexit 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= min ✓ sup f2B R fd↵✓ 1 m P j f(yj) <latexit 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<latexit 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= min ✓ sup f2B R f(g✓(z))d⇣ 1 m P j f(yj) <latexit 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{f⇠ }⇠ ⇢ B <latexit 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<latexit 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<latexit 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min ✓ sup ⇠ R f⇠(g✓(z))d⇣ P j f⇠(yj) <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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  34. Semi-discrete Problem = Pm j=1 bj yj y1 <latexit sha1_base64="t5eybmmsf+EgOiAsv/fpA0yXp0U=">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</latexit>

    <latexit 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↵ Optimal Monge map: <latexit 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<latexit 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T : Lj 7 ! yj <latexit 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<latexit 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<latexit 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L1 <latexit 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  35. Semi-discrete Problem = Pm j=1 bj yj y1 <latexit sha1_base64="t5eybmmsf+EgOiAsv/fpA0yXp0U=">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</latexit>

    <latexit 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↵ Optimal Monge map: <latexit 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<latexit 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T : Lj 7 ! yj <latexit 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0 0.5 1 -0.2 0 0.2 0.4 0.6 0.5 1 1.5 2 p = 1/2 p = 1 p = 3/2 p = 2 Figure 5.1: Top: examples of semi-discrete ¯ c-transforms g ¯ c in 1-D, for ground cost c(x, y) = |x ≠ y|p for varying p (see colorbar). The red points are at locations (yj, ≠gj ) j . Bottom: examples of semi-discrete ¯ c-transforms g ¯ c in 2-D, for ground cost c(x, y) = Îx ≠ yÎp for varying p. The red points are at locations yj œ R2 , and their size is proportional to gj . The regions delimited by bold black curves are the Laguerre cells (Lg(yj )) j associated to these points (yj ) j . 0 0.5 1 -0.2 0 0.2 0.4 0.6 p = 1/2 p = 1 p = 3/2 Figure 5.1: Top: examples of semi-discrete ¯ c-transforms g ¯ c cost c(x, y) = |x ≠ y|p for varying p (see colorbar). The red poi (yj, ≠gj ) j . Bottom: examples of semi-discrete ¯ c-transforms g ¯ c cost c(x, y) = Îx ≠ yÎp for varying p. The red points are at loc their size is proportional to gj . The regions delimited by bold b Laguerre cells (Lg(yj )) j associated to these points (yj ) j . c(x, y) = ||x y|| <latexit 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<latexit 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c(x, y) = ||x y||2 <latexit 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<latexit 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<latexit 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<latexit 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L1 <latexit 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<latexit 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c-transform: <latexit 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<latexit 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gc(x) def. = min 16j6m c(x, yj) gj <latexit 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<latexit 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  36. Semi-discrete Problem = Pm j=1 bj yj y1 <latexit sha1_base64="t5eybmmsf+EgOiAsv/fpA0yXp0U=">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</latexit>

    <latexit 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↵ Optimal Monge map: <latexit 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<latexit 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T : Lj 7 ! yj <latexit 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<latexit 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max g2Rm E(g) def. = R gc(x)(x)d↵(x) + P j gjbj <latexit 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<latexit 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Semi-discrete OT: <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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0 0.5 1 -0.2 0 0.2 0.4 0.6 0.5 1 1.5 2 p = 1/2 p = 1 p = 3/2 p = 2 Figure 5.1: Top: examples of semi-discrete ¯ c-transforms g ¯ c in 1-D, for ground cost c(x, y) = |x ≠ y|p for varying p (see colorbar). The red points are at locations (yj, ≠gj ) j . Bottom: examples of semi-discrete ¯ c-transforms g ¯ c in 2-D, for ground cost c(x, y) = Îx ≠ yÎp for varying p. The red points are at locations yj œ R2 , and their size is proportional to gj . The regions delimited by bold black curves are the Laguerre cells (Lg(yj )) j associated to these points (yj ) j . 0 0.5 1 -0.2 0 0.2 0.4 0.6 p = 1/2 p = 1 p = 3/2 Figure 5.1: Top: examples of semi-discrete ¯ c-transforms g ¯ c cost c(x, y) = |x ≠ y|p for varying p (see colorbar). The red poi (yj, ≠gj ) j . Bottom: examples of semi-discrete ¯ c-transforms g ¯ c cost c(x, y) = Îx ≠ yÎp for varying p. The red points are at loc their size is proportional to gj . The regions delimited by bold b Laguerre cells (Lg(yj )) j associated to these points (yj ) j . c(x, y) = ||x y|| <latexit 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<latexit 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c(x, y) = ||x y||2 <latexit 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<latexit 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<latexit 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<latexit 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L1 <latexit 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<latexit 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c-transform: <latexit 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<latexit 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gc(x) def. = min 16j6m c(x, yj) gj <latexit 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<latexit 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  37. Semi-discrete Problem = Pm j=1 bj yj y1 <latexit sha1_base64="t5eybmmsf+EgOiAsv/fpA0yXp0U=">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</latexit>

    <latexit 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↵ Optimal Monge map: <latexit 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<latexit 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T : Lj 7 ! yj <latexit 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<latexit 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max g2Rm E(g) def. = R gc(x)(x)d↵(x) + P j gjbj <latexit 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<latexit 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Semi-discrete OT: <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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0 0.5 1 -0.2 0 0.2 0.4 0.6 0.5 1 1.5 2 p = 1/2 p = 1 p = 3/2 p = 2 Figure 5.1: Top: examples of semi-discrete ¯ c-transforms g ¯ c in 1-D, for ground cost c(x, y) = |x ≠ y|p for varying p (see colorbar). The red points are at locations (yj, ≠gj ) j . Bottom: examples of semi-discrete ¯ c-transforms g ¯ c in 2-D, for ground cost c(x, y) = Îx ≠ yÎp for varying p. The red points are at locations yj œ R2 , and their size is proportional to gj . The regions delimited by bold black curves are the Laguerre cells (Lg(yj )) j associated to these points (yj ) j . 0 0.5 1 -0.2 0 0.2 0.4 0.6 p = 1/2 p = 1 p = 3/2 Figure 5.1: Top: examples of semi-discrete ¯ c-transforms g ¯ c cost c(x, y) = |x ≠ y|p for varying p (see colorbar). The red poi (yj, ≠gj ) j . Bottom: examples of semi-discrete ¯ c-transforms g ¯ c cost c(x, y) = Îx ≠ yÎp for varying p. The red points are at loc their size is proportional to gj . The regions delimited by bold b Laguerre cells (Lg(yj )) j associated to these points (yj ) j . c(x, y) = ||x y|| <latexit 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<latexit 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c(x, y) = ||x y||2 <latexit 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<latexit 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<latexit 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<latexit 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L1 <latexit 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<latexit 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c-transform: <latexit 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<latexit 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gc(x) def. = min 16j6m c(x, yj) gj <latexit 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<latexit 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Laguerre cells: <latexit 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Lj(g) def. = x ; 8`, c(x, yj) gj 6 c(x, y`) g` <latexit 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<latexit 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  38. Semi-discrete Problem = Pm j=1 bj yj y1 <latexit sha1_base64="t5eybmmsf+EgOiAsv/fpA0yXp0U=">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</latexit>

    <latexit 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↵ Optimal Monge map: <latexit 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<latexit 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T : Lj 7 ! yj <latexit 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<latexit 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max g2Rm E(g) def. = R gc(x)(x)d↵(x) + P j gjbj <latexit 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<latexit 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Semi-discrete OT: <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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0 0.5 1 -0.2 0 0.2 0.4 0.6 0.5 1 1.5 2 p = 1/2 p = 1 p = 3/2 p = 2 Figure 5.1: Top: examples of semi-discrete ¯ c-transforms g ¯ c in 1-D, for ground cost c(x, y) = |x ≠ y|p for varying p (see colorbar). The red points are at locations (yj, ≠gj ) j . Bottom: examples of semi-discrete ¯ c-transforms g ¯ c in 2-D, for ground cost c(x, y) = Îx ≠ yÎp for varying p. The red points are at locations yj œ R2 , and their size is proportional to gj . The regions delimited by bold black curves are the Laguerre cells (Lg(yj )) j associated to these points (yj ) j . 0 0.5 1 -0.2 0 0.2 0.4 0.6 p = 1/2 p = 1 p = 3/2 Figure 5.1: Top: examples of semi-discrete ¯ c-transforms g ¯ c cost c(x, y) = |x ≠ y|p for varying p (see colorbar). The red poi (yj, ≠gj ) j . Bottom: examples of semi-discrete ¯ c-transforms g ¯ c cost c(x, y) = Îx ≠ yÎp for varying p. The red points are at loc their size is proportional to gj . The regions delimited by bold b Laguerre cells (Lg(yj )) j associated to these points (yj ) j . c(x, y) = ||x y|| <latexit 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<latexit 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c(x, y) = ||x y||2 <latexit 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<latexit 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<latexit 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<latexit 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L1 <latexit 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<latexit 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c-transform: <latexit 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<latexit 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gc(x) def. = min 16j6m c(x, yj) gj <latexit 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<latexit 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Laguerre cells: <latexit 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Lj(g) def. = x ; 8`, c(x, yj) gj 6 c(x, y`) g` <latexit 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<latexit 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sha1_base64="61va2ofxDDf/6ykQJswY8pEset8=">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</latexit> Proposition: <latexit 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<latexit 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sha1_base64="PiBtOOTAAUJsxdt5ASuoHfK8+mY=">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</latexit> rE(g)j = R Lj (g) d↵ + bj <latexit 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<latexit 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  39. Gradient descent: <latexit 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<latexit 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<latexit 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g (1 ⌧)g + ⌧ R Lj (g) d↵ <latexit 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<latexit 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<latexit 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Franz Aurenhammer Quentin Mérigot Vladimir Oliker Bruno Levy Semi-discrete Optimization <latexit 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! In practice: use quasi-Newton (L-BFGS).
  40. Gradient descent: <latexit 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<latexit 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<latexit 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g (1 ⌧)g + ⌧ R Lj (g) d↵ <latexit 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<latexit 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<latexit 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Franz Aurenhammer Quentin Mérigot Vladimir Oliker Bruno Levy Semi-discrete Optimization <latexit 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! In practice: use quasi-Newton (L-BFGS).
  41. Optimal Quantization ↵ = P j bj yj <latexit sha1_base64="J/UT0rKb/egZhQXgBj4nhb0pjSg=">AABB7HictVzdchu3FYbTv9j9c9rL3mwru+NkHFdSM9POZDITWZJlxbRNh5TsJLQ1XHJFU15yaS4p/zB8h170rtPbPkJv09foG7RXfYWeH2CBJbELQHWNkYQF8Z1zcBY4OOcAdDxJh/lsc/Ofl9773vd/8MMfvX/5yo9/8tOf/fzqB784zrP5tJcc9bI0mz6Ju3mSDsfJ0Ww4S5Mnk2nSHcVp8jh+sYufPz5PpvkwG7dnbybJ01F3MB6eDnvdGTSdXP3oWoeILOJ0niyjTpxEn0WdfD46OYMH/NVPThZvTs6W106ubmze2qR/0XplS1Y2hPzXzD6IjkRH9EUmemIuRiIRYzGDeiq6IofyjdgSm2ICbU/FAtqmUBvS54lYiiuAnUOvBHp0ofUF/B7A0zeydQzPSDMndA+4pPAzBWQkrgMmg35TqCO3iD6fE2VsraK9IJoo2xv4G0taI2idiefQ6sKpnr44HMtMnIo/0hiGMKYJteDoepLKnLSCkkfGqGZAYQJtWO/D51Oo9wip9BwRJqexo2679Pm/qCe24nNP9p2Lf5OU16FEoiVHnxUUuuKc6Ef0NufwGcuTAucBUEjkGLH2inQ9otGPof8C2h9AWVJN6SSGsqDWZS1yF4oNuetEHkCxIQ+cyAYUG7LhRDah2JBNiUTslHRux7eg2PAtJ+dHUGzIR07kl1BsyC+dyGMoNuSxE/k1FBvyayfyDhQb8o4TeQ+KDXnPiWxDsSHbTuQRFBvyyInch2JD7ktk9UqdQsmIztCxKnegXuaBliKFlh2nfLfJOtqwtz3WdK8C617Ve/DXjt3z0GlSgd33mHenFVj3zDsAG2nHum3RXdpNbNi7TuwhzAA79tCJ/UKcVWC/8FhpLyqw7rXWgH52rNv63ocnO/a+E/sAanase496CC127EOPHWNSgW06sY/Eywqsj9WfVmDddr8FdsWOde9Tbehvx/pY03kF1m1Pj8GDsWPdu9VjaLVjHzuxT8TrCuwTJ/YrsO527FceO+zbCqzaY6/QDjIgfySBFVtHrVusSqxNgFrXwT8t9paUfOMY2l2YQYEZEGbkRBwUiANPRKNANLzlygs7mpO/6+bSKhAtT0Rc7E1Ymzn794v+WEs9EHsFYm8FUeeR4rtWYzkn70K1uJCzYufCms+YssJ+Yy2R86He8irEwxKC5/Zzmvk3KVrCCAo1VUftebHHMzKi5zrEK4re1CgVDzduVlgFE/XaiYotqNiJemNBvXGi5hbU3Ik6t6DOnSi98k1cx2MGaP3ju1jQE88A9pGrSwRewQ7sOndhjUYwf5rgBX5JLQ/hb4tib1epkwyjedwnMcvxtGSJp1BbiA1o11HhHsXXKa2wBCTjng9ljI9PmNtYyDXHVnhZ7ORRkTHxpzMkeQYFHfQWI1pPYXTuUcuSvDuuheHvFute1cLw+6TxJXnxXAvDz6T0swvI3pbY9gWwLVhNE6l9XQ+lwfkXpqHqV2jXRYuLb3Uk5wzSex1I/1C+mcMLvJddqrF+dD2MRm6MLy+NL4SG1nNu6DmMCnpP7PWqWhQ8krGMe3U9VIaMdtGxlEM/hb4Z7NOXb0bVw2g0wePapZh7YdRDZ++kGI2uh9E4Fpz3XJInr+phNAb0zPrQ9TAamG3pyjhf10MtO2qAY2ddD7XqY8oCYw6I5zy3aK9oSn7SXFIbkn9Qn60xff71fQxzNs+KGKGekvZtq+nExV5WL5HyFxKwarNAOdC/mBs+WJnGQmw74yuWYVba39fp6D0eNd8ALUaw+vkMwJUzT0FClZNA650CxS1n1FUemcJtO3E4S05XUB3ZOnN6i5ovZ43KbSfU6orL9Gi1Hjtkr3OaexPyCRukWZceGpVvuIqiS0ONkobc9EJ091au17L2N524yQpiUsy0Hp0I8UlafZxq03rL0PF1ecozg8JnPnr+Yrb5VFobjHkyskUoSx1Ps5/KI5ltuK/eFDrHzZ9F9EbRXp2T1RjSiVTujEJVtpi98QU9a9pHdCaHPJhGD95jJKlMBJ+aYRYd8+kRWVTT3rp4o75Uho7rOVldZY/r0QMDPbCgw2OcXdgxHkCtDTHDETy1PaKcK4WuMtL4VHxcnI5m9AbrI/q0ZCEVDbY3SclC1kXZz0tUXgEaZwNH6f40VukofGeNkjvqt8mjY9ey5b9OJ7fqfLtLc7x6NldnYvrEdZu4RrRq+FSXn1Y5sAQL6yfb5L/WjxL5hXBEG+ri+szgzHoZ04l/QhHshDzjlFaba3WUe5v5qdVPFKemUGfneJqdkYWMyP5FsD9lNCcj+jHvDqgTdLYIKdlIH7szLLwbm68zdM4x7ccNBd9q0PMtIVs2J/6Krrm6cpqLHDHwPrBcmdtKJw3yBRPiOpXWXa/t+t0HkfqehDlLmKKeKzeI/4f0W/2oebKxNiNQw/gGcmnrbO8jo5gFddSlXb7eBqm+ppTXChmeSan1/qdlulaSbI8iLpQHd+s+cO7RM/PCWTIlufO1PryP1mVzkfJkRY842lOK4tnuD+QOjHLfpF1yg9Zch2bJAGbBrIgiVF9XFnmVbz2vMnU/2vn/hbrWdVlrSDESOoPLGnLl9xOK1kwpU5jVPH9f0Gqya3260quez5jm4shYy99C66/ht5JbPfvRiUtW4TbNAaagn7RGuCVa6+HH63aJl5qZipZ+1vz0nFS9zJaLxNds3XSMfR5MpUmz5rXMWqj6RWicGTTOPHXYprNGrUXVrizRiTO2aMvTSl9+IdzaAZTnTspuj0yhhh5SmrGUH9W+k6o7xleot05am05aXVit5mmAueZ9kPa1vrq6vy1290jcId+mRx4Yxy99WqVD8rlUa32kxhSQ8yfSvpqrv0MtyD0mC4qU+R4nrhg+depRWRaS/lbubBnZeW0R1L2lV7KPsrEdqv9+DTmiNZHTulSIT6hHIuU35YhWLNItw+eIKPPfJZ+K/Y76mNnsrd9JVPIndLzJq0rz4khhTPp3Zd4O16LXQyN+jSgmnEvvOgZa4W8YKTBGZRLsnmVObwh3OT5JYI82Jvu5bqf4FG9sSHSLpF6IzzxsDEe9eq6bc0uNWI3tI+iJWtdv3dbDzS/15ujid5ETvS7taiPpoy5Wni9Gqyt3ufJznR7mK3y1PubUx4wsdJRXxnTEp95cWKIwLozx4RI2ihD5wyQPkZlPp3wpq96KcjnTwDbmOcVLrnugiLB5dzes3tyHjnHEa/RiwprUuMVFCbNxmcwPmJYWs1KX1/Yhbr1cuxulxk5UtVMo6uZuoe03W8iErF8qXDkb7m3K3ilFKe4sDFPoCb7RWxUfmjQ/hYK/I2GLDhVHn9xhC/zbHbEr9t/BbYiXss4ZzYha0Bb0V2LvrhxnuUe9jl4a1E36Phz8eQxB1y7ph7SThsrOlN2Sm9T96b8iKzAViVN63TN8DCYX90jWOYWMZ0iWzT2aoVDfxQkdi+LgM5IyF38+fK7hGsWpUN9pChuDou4eQZlDCA91j8Hvneve4bxMTvX6Wufiy4N3AXXionB48lcdq+h+PhZqaryRd88BrcNpDXW1W/yv41B8NKdwXr7ccvqu2ZnHW+d+iczIoj8cvmY0N5/ZXM3Rn2dWjE57S3Z+7PdFQW8qM0bz7umjP6rngOK1EJwHdUvHeHMWaXl9qeC5gE2GTPxHfHfJ/W2ElwWNKjlCKKlzimpqqoebmvrGpW106jMfmTSdKpnK1HQc0aIbsbviUNyBn93CAwy9HcrfpeS/iLV/f7YPradkPVQWnTMHHWpLKPuhT9H69Kzvz1ZJjHd5+W5vG1rwLLxBrXjP9wH1x7u+7dLYqr9Bwmv9vshEvxSRrJ7u6XUVwwjKJ2+cA1Lf843oLj1nsfjm2cjjbFHdn1qVaEGfuG8WxJX42JCyR3N1Is/q8eQAb9h3i/xQJH5HbV1p53HPdXFuVnJurnDOSTtlDq+Nz+rvZlVx2TW49Ivc2bnsl1Gcrc/z6nOje5Vc+A56PX5Qgx8YUrZI+y8oEp6K+mzevIbmXMpknrCOhcpEsh4wzuwW77s+sj2v4XXuMf57leh7hqQHIEtM+e+ITtimRC+Vutkn6fmmY30m9W6NtPJ7lCdXN7ZW/y+D9crx9q2tzVtbj7Y3Pr8t/5+D98WvxG/EDVjjfxCfA7WmOAIOfxJ/F9+Jf+yMd/6885edv3LX9y5JzC9F6d/O3/4LH5mxDw==</latexit>

    <latexit 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<latexit 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<latexit 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quantization <latexit 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<latexit sha1_base64="Pv8Yn3B5GzNCGZ4ksVEmu3Zl+xk=">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</latexit> Qm(↵) def. = min b, Y Wp(↵, P j bj yj ) <latexit 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<latexit 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  42. Optimal Quantization ↵ = P j bj yj <latexit sha1_base64="J/UT0rKb/egZhQXgBj4nhb0pjSg=">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</latexit>

    <latexit 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<latexit 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<latexit 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quantization <latexit 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sha1_base64="Pv8Yn3B5GzNCGZ4ksVEmu3Zl+xk=">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</latexit> convex <latexit 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<latexit 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<latexit sha1_base64="HL+CWgVEA+ho9MS6+Yq/V1Xlz0w=">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</latexit> non-convex <latexit 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<latexit 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<latexit sha1_base64="VdRImCsKpMsG7hpSphWq5LcEdys=">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</latexit> Qm(↵) def. = min b, Y Wp(↵, P j bj yj ) <latexit 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<latexit 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  43. Optimal Quantization ↵ = P j bj yj <latexit sha1_base64="J/UT0rKb/egZhQXgBj4nhb0pjSg=">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</latexit>

    <latexit 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<latexit 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<latexit 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quantization <latexit 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sha1_base64="Pv8Yn3B5GzNCGZ4ksVEmu3Zl+xk=">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</latexit> convex <latexit 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<latexit 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<latexit sha1_base64="HL+CWgVEA+ho9MS6+Yq/V1Xlz0w=">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</latexit> non-convex <latexit 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<latexit 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<latexit sha1_base64="VdRImCsKpMsG7hpSphWq5LcEdys=">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</latexit> In general: Qm(↵) ⇠ 1/m1/d. <latexit 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<latexit 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sha1_base64="MHuuTNavetQqrQWov3mo3dZHRy4=">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</latexit> Qm(↵) def. = min b, Y Wp(↵, P j bj yj ) <latexit 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<latexit 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  44. Optimal Quantization ↵ = P j bj yj <latexit sha1_base64="J/UT0rKb/egZhQXgBj4nhb0pjSg=">AABB7HictVzdchu3FYbTv9j9c9rL3mwru+NkHFdSM9POZDITWZJlxbRNh5TsJLQ1XHJFU15yaS4p/zB8h170rtPbPkJv09foG7RXfYWeH2CBJbELQHWNkYQF8Z1zcBY4OOcAdDxJh/lsc/Ofl9773vd/8MMfvX/5yo9/8tOf/fzqB784zrP5tJcc9bI0mz6Ju3mSDsfJ0Ww4S5Mnk2nSHcVp8jh+sYufPz5PpvkwG7dnbybJ01F3MB6eDnvdGTSdXP3oWoeILOJ0niyjTpxEn0WdfD46OYMH/NVPThZvTs6W106ubmze2qR/0XplS1Y2hPzXzD6IjkRH9EUmemIuRiIRYzGDeiq6IofyjdgSm2ICbU/FAtqmUBvS54lYiiuAnUOvBHp0ofUF/B7A0zeydQzPSDMndA+4pPAzBWQkrgMmg35TqCO3iD6fE2VsraK9IJoo2xv4G0taI2idiefQ6sKpnr44HMtMnIo/0hiGMKYJteDoepLKnLSCkkfGqGZAYQJtWO/D51Oo9wip9BwRJqexo2679Pm/qCe24nNP9p2Lf5OU16FEoiVHnxUUuuKc6Ef0NufwGcuTAucBUEjkGLH2inQ9otGPof8C2h9AWVJN6SSGsqDWZS1yF4oNuetEHkCxIQ+cyAYUG7LhRDah2JBNiUTslHRux7eg2PAtJ+dHUGzIR07kl1BsyC+dyGMoNuSxE/k1FBvyayfyDhQb8o4TeQ+KDXnPiWxDsSHbTuQRFBvyyInch2JD7ktk9UqdQsmIztCxKnegXuaBliKFlh2nfLfJOtqwtz3WdK8C617Ve/DXjt3z0GlSgd33mHenFVj3zDsAG2nHum3RXdpNbNi7TuwhzAA79tCJ/UKcVWC/8FhpLyqw7rXWgH52rNv63ocnO/a+E/sAanase496CC127EOPHWNSgW06sY/Eywqsj9WfVmDddr8FdsWOde9Tbehvx/pY03kF1m1Pj8GDsWPdu9VjaLVjHzuxT8TrCuwTJ/YrsO527FceO+zbCqzaY6/QDjIgfySBFVtHrVusSqxNgFrXwT8t9paUfOMY2l2YQYEZEGbkRBwUiANPRKNANLzlygs7mpO/6+bSKhAtT0Rc7E1Ymzn794v+WEs9EHsFYm8FUeeR4rtWYzkn70K1uJCzYufCms+YssJ+Yy2R86He8irEwxKC5/Zzmvk3KVrCCAo1VUftebHHMzKi5zrEK4re1CgVDzduVlgFE/XaiYotqNiJemNBvXGi5hbU3Ik6t6DOnSi98k1cx2MGaP3ju1jQE88A9pGrSwRewQ7sOndhjUYwf5rgBX5JLQ/hb4tib1epkwyjedwnMcvxtGSJp1BbiA1o11HhHsXXKa2wBCTjng9ljI9PmNtYyDXHVnhZ7ORRkTHxpzMkeQYFHfQWI1pPYXTuUcuSvDuuheHvFute1cLw+6TxJXnxXAvDz6T0swvI3pbY9gWwLVhNE6l9XQ+lwfkXpqHqV2jXRYuLb3Uk5wzSex1I/1C+mcMLvJddqrF+dD2MRm6MLy+NL4SG1nNu6DmMCnpP7PWqWhQ8krGMe3U9VIaMdtGxlEM/hb4Z7NOXb0bVw2g0wePapZh7YdRDZ++kGI2uh9E4Fpz3XJInr+phNAb0zPrQ9TAamG3pyjhf10MtO2qAY2ddD7XqY8oCYw6I5zy3aK9oSn7SXFIbkn9Qn60xff71fQxzNs+KGKGekvZtq+nExV5WL5HyFxKwarNAOdC/mBs+WJnGQmw74yuWYVba39fp6D0eNd8ALUaw+vkMwJUzT0FClZNA650CxS1n1FUemcJtO3E4S05XUB3ZOnN6i5ovZ43KbSfU6orL9Gi1Hjtkr3OaexPyCRukWZceGpVvuIqiS0ONkobc9EJ091au17L2N524yQpiUsy0Hp0I8UlafZxq03rL0PF1ecozg8JnPnr+Yrb5VFobjHkyskUoSx1Ps5/KI5ltuK/eFDrHzZ9F9EbRXp2T1RjSiVTujEJVtpi98QU9a9pHdCaHPJhGD95jJKlMBJ+aYRYd8+kRWVTT3rp4o75Uho7rOVldZY/r0QMDPbCgw2OcXdgxHkCtDTHDETy1PaKcK4WuMtL4VHxcnI5m9AbrI/q0ZCEVDbY3SclC1kXZz0tUXgEaZwNH6f40VukofGeNkjvqt8mjY9ey5b9OJ7fqfLtLc7x6NldnYvrEdZu4RrRq+FSXn1Y5sAQL6yfb5L/WjxL5hXBEG+ri+szgzHoZ04l/QhHshDzjlFaba3WUe5v5qdVPFKemUGfneJqdkYWMyP5FsD9lNCcj+jHvDqgTdLYIKdlIH7szLLwbm68zdM4x7ccNBd9q0PMtIVs2J/6Krrm6cpqLHDHwPrBcmdtKJw3yBRPiOpXWXa/t+t0HkfqehDlLmKKeKzeI/4f0W/2oebKxNiNQw/gGcmnrbO8jo5gFddSlXb7eBqm+ppTXChmeSan1/qdlulaSbI8iLpQHd+s+cO7RM/PCWTIlufO1PryP1mVzkfJkRY842lOK4tnuD+QOjHLfpF1yg9Zch2bJAGbBrIgiVF9XFnmVbz2vMnU/2vn/hbrWdVlrSDESOoPLGnLl9xOK1kwpU5jVPH9f0Gqya3260quez5jm4shYy99C66/ht5JbPfvRiUtW4TbNAaagn7RGuCVa6+HH63aJl5qZipZ+1vz0nFS9zJaLxNds3XSMfR5MpUmz5rXMWqj6RWicGTTOPHXYprNGrUXVrizRiTO2aMvTSl9+IdzaAZTnTspuj0yhhh5SmrGUH9W+k6o7xleot05am05aXVit5mmAueZ9kPa1vrq6vy1290jcId+mRx4Yxy99WqVD8rlUa32kxhSQ8yfSvpqrv0MtyD0mC4qU+R4nrhg+depRWRaS/lbubBnZeW0R1L2lV7KPsrEdqv9+DTmiNZHTulSIT6hHIuU35YhWLNItw+eIKPPfJZ+K/Y76mNnsrd9JVPIndLzJq0rz4khhTPp3Zd4O16LXQyN+jSgmnEvvOgZa4W8YKTBGZRLsnmVObwh3OT5JYI82Jvu5bqf4FG9sSHSLpF6IzzxsDEe9eq6bc0uNWI3tI+iJWtdv3dbDzS/15ujid5ETvS7taiPpoy5Wni9Gqyt3ufJznR7mK3y1PubUx4wsdJRXxnTEp95cWKIwLozx4RI2ihD5wyQPkZlPp3wpq96KcjnTwDbmOcVLrnugiLB5dzes3tyHjnHEa/RiwprUuMVFCbNxmcwPmJYWs1KX1/Yhbr1cuxulxk5UtVMo6uZuoe03W8iErF8qXDkb7m3K3ilFKe4sDFPoCb7RWxUfmjQ/hYK/I2GLDhVHn9xhC/zbHbEr9t/BbYiXss4ZzYha0Bb0V2LvrhxnuUe9jl4a1E36Phz8eQxB1y7ph7SThsrOlN2Sm9T96b8iKzAViVN63TN8DCYX90jWOYWMZ0iWzT2aoVDfxQkdi+LgM5IyF38+fK7hGsWpUN9pChuDou4eQZlDCA91j8Hvneve4bxMTvX6Wufiy4N3AXXionB48lcdq+h+PhZqaryRd88BrcNpDXW1W/yv41B8NKdwXr7ccvqu2ZnHW+d+iczIoj8cvmY0N5/ZXM3Rn2dWjE57S3Z+7PdFQW8qM0bz7umjP6rngOK1EJwHdUvHeHMWaXl9qeC5gE2GTPxHfHfJ/W2ElwWNKjlCKKlzimpqqoebmvrGpW106jMfmTSdKpnK1HQc0aIbsbviUNyBn93CAwy9HcrfpeS/iLV/f7YPradkPVQWnTMHHWpLKPuhT9H69Kzvz1ZJjHd5+W5vG1rwLLxBrXjP9wH1x7u+7dLYqr9Bwmv9vshEvxSRrJ7u6XUVwwjKJ2+cA1Lf843oLj1nsfjm2cjjbFHdn1qVaEGfuG8WxJX42JCyR3N1Is/q8eQAb9h3i/xQJH5HbV1p53HPdXFuVnJurnDOSTtlDq+Nz+rvZlVx2TW49Ivc2bnsl1Gcrc/z6nOje5Vc+A56PX5Qgx8YUrZI+y8oEp6K+mzevIbmXMpknrCOhcpEsh4wzuwW77s+sj2v4XXuMf57leh7hqQHIEtM+e+ITtimRC+Vutkn6fmmY30m9W6NtPJ7lCdXN7ZW/y+D9crx9q2tzVtbj7Y3Pr8t/5+D98WvxG/EDVjjfxCfA7WmOAIOfxJ/F9+Jf+yMd/6885edv3LX9y5JzC9F6d/O3/4LH5mxDw==</latexit>

    <latexit 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<latexit 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<latexit 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quantization <latexit 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sha1_base64="Pv8Yn3B5GzNCGZ4ksVEmu3Zl+xk=">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</latexit> convex <latexit 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<latexit 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<latexit sha1_base64="HL+CWgVEA+ho9MS6+Yq/V1Xlz0w=">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</latexit> non-convex <latexit 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<latexit 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<latexit sha1_base64="VdRImCsKpMsG7hpSphWq5LcEdys=">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</latexit> In general: Qm(↵) ⇠ 1/m1/d. <latexit 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<latexit 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Qm(↵) = <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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min Y max g2Rm R gc(x)(x)d↵(x) + min b P j gjbj <latexit 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sha1_base64="ltLLjI8KzYMVc1XIIjXd55ioYYA=">AABGIXictVxfc9u4EYev/y7uv6R97At7TjpJL83Z7nWu05vOJLEdxxcncSLZ+afEQ0q0IocSFUlUnOj0afrYD9HnvnX61ukXaJ/6Fbq7AAhQArmgm4ZnGwTx210sgcXuArxomPTGk/X1f6x88p3vfu/7P/j0wuoPf/Tjn/z04qWfHY3TbNSOD9tpko6eRuE4TnqD+HDSmyTx0+EoDvtREj+J3mzh8yfTeDTupYPm5P0wftkPu4PeSa8dTqDq+OKfL7eyfm8waxGpWZRk8Tx4Ng+gNjybFapbR3F7cj/txLPuHBr0BkHr8eNX/XmwCuVJUN72Vfvq2TX4L2h1WmGChdXPA8U2AkrjrH98WoGHh63o+PTy8cW19Rvr9C9YLmyowppQ/w7SS599IVqiI1LRFpnoi1gMxATKiQjFGK4XYkOsiyHUvRQzqBtBqUfPYzEXq4DNoFUMLUKofQO/u3D3QtUO4B5pjgndBi4J/IwAGYgrgEmh3QjKyC2g5xlRxtoy2jOiibK9h7+RotWH2ol4DbUcTrf0xWFfJuJE/J760IM+DakGe9dWVDLSCkoeWL2aAIUh1GG5A89HUG4TUus5IMyY+o66Den5v6gl1uJ9W7XNxL9JyitwBaKhep/mFEIxJfoBvc0Mnkl5EuDcBQqx6iOW3pGu+9T7AbSfQf0DuOZU0jqJ4JpR7bwSuQWXC7nFInfhciF3WeQ+XC7kPos8gMuFPFBIxI5I5258Ay4XvsFyfgSXC/mIRT6Gy4V8zCKP4HIhj1jkc7hcyOcs8g5cLuQdFnkPLhfyHotswuVCNlnkIVwu5CGL3IHLhdxRyPKZOoIrJTo9ZlbegnKRB1qKBGpusfLdJuvowt72mNPtEiw/q7fhrxu77aHTuAS74zHuTkqw/MjbBRvpxvK26C6tJi7sXRa7ByPAjd1jsd+I0xLsNx4z7U0Jlp9r+9DOjeWt7324c2Pvs9gHUHJj+TXqIdS4sQ89VoxhCfaAxT4Sb0uwPlZ/VILl7X4D7Ioby69TTWjvxvpY06wEy9vTI/Bg3Fh+tXoCtW7sExb7VJwRFsvGR52RF4CWbJnmU6JZTfUZ2H0XVfTLMrJyy3SfedB9Lj6U9FSvzKu07nRJ/hjmeRW1UM3l8r5jiyFwCVnJknytSsjXjqA+ZDDdHNMlTJ9F7OaIXU/Efo7Y95ZrnNvlMfnPPJdGjmh4IiK11lWNEGwz8dB9J183sZQoTPUqrRHbC4gq7xdHgu7nlDwZXcMhJ/kqiaXYQ8I0XyuwFKuxUm3lNeJhASFnxGuaL9cpMsNoDTVVRe117k9IZED3VYh3FCnqXmoePG6iLFARdcaiIgcqYlHvHaj3LCpzoDIWNXWgpizKWAUb1/IYAUb/+C5mdCdHgPTHy68APJBbsMLdhfkbwPg5AI/zMdU8hL8NivO5q0oyzBzgmowZlZcF+z2C0kysQb2JQLcplk9ohsUgmWz5UOUT8E7aCjnnpI2e515DkGdn/On0SJ5uTgc904DmUz0696hmTp6kLNXD383nvS7Vw++QxhGvS/XwEyX95ByyNxW2eQ5sA2bTUGnflOvSkLkeSUOXV2lFRouLb7WvxgzSO6tJf0+9mb1zvJctKkn9mHI9GmOrf+NC/+rQMHoeW3quRwV9Lulh61JQuycDFWObcl0ZUlpFB0oOc1f3zWCbjnozulyPxgF4Y1sU38+sct3RO8x7Y8r1aBwJmWOdU9Sgy/VodOle6sOU69HAzE6ocgqmXNeyowZknG7Kda36gDLOmG+SY17WGK9oRH5Spqj1yD+ozgzZEcHyOob5oVdCRxbVlIx3W04nyteyaom0vxCDVZvUlAP9i8zywYo0ZmKT9b+lDJPC+r5Mx6zxqPl90GIAs1/uN3D5eYwJdP4DrXcCFDfYiKzYM43bZHE4Sk4WUC1VO2G9RcP3NI9wTN0x1XIxm+mt0WOL7PWYxt6QfMJ90iynh/3SN1xGkdPQfkFDPL06uvug5mtR++ssbriAGOYjrU27T3LXrjqGdWm9Yen4itpRmsAl95fM+MXM9omyNhjzpGSLUJYqnnY7nbOy63BdvS5MPl0+C+iNor2aktXo0e7XmI1CdWZaeuMzuje0D2n/D3lIGm14j4GiMhRyhw4z9pi7D8ii2vaW44360tlAWR6T1dX2uBrdtdBdB7p+jLMFK8YDKDUhZjiEu6ZHlLOa6yoljY/Eb/Kd2JTeYHVEnxQspKYh7U1csJBVUfbrApV3gMbRIKN0fxqLdDS+tUSJj/pd8pjYtWj5r9Ausd5LD2mMl4/m8kxMh7huEteAZo3cQZZ3ixykBDPnk03yX6t7ifzqcEQbynF9ZXGWehnQ6YKYItghecYJzTZudhRb2/mpxSea04HQ+/S4c56ShQzI/gWwPqU0JgP6sc8p6N16aRESspE+dqeXezcuX6fHjjHjx/WEPEFhxltMtiwj/pquPbvGNBZlxCDXgfnC2NY62SdfMCauI2XdzdyuXn0Qac5k2KNEUjRj5Srxv0a/9Y8eJ2tLIwI1jG9grGyd632kFLOgjkJa5attkG5rS3k5l+GVktqsf0amywXJtiniQnlwte4A5zbdS144SkYk93ipjVxHq7K5SHm4oEfs7QlF8dLud9UKjHJfp1VyjeZci0ZJF0bBJI8idFsui7zIt5pXkbof7fH/hbrRdVFrSDEQJoMrNcTl/mOK1mwpExjVcvy+odnk1vpooVU1nwGNxb41l7+F2l/Cby23vvejExWswm0aA5KCuTMakTXBUgs/XrcLvPTI1LTMveFnxqRuZdecJ76W1s3E2NPaVA5o1JyprIUun4fGqUXj1FOHTdrXNFrU9doSHbOxRVPtjPryq8OtWYNyxlLmPTKN6nlIacdSflQ7LFU+xteoDyytdZZWCLPV3g2w57wP0j3XF2f3t/nqHog75Nu0yQOT8UuHZmmPfC5dWx2pSQrI+UtlX+3Z36Ia5B6RBUXK8swozhi569Sma55L+iu1sqVk541F0Gek3qk22sa2qPzbJWSf5sSY5qVGfEktYiW/LUewYJFuWD5HQJn/kHwq6XdUx8x2a/NOgoI/YeJNOasMLxkpDEj/XOZtbyl63bPi14Biwkx51xHQqv+GkYLE6EyC27Mc0xvCVU7uJEiPNiL7uWyn5C7ewJLoBkk9E3/0sDEy6jVj3R5buse6b7+Glqh189ZdLXh+iTdHjt95dvRCWtX6ykedLdyfj1aoVrnifZUesgW+Rh8ZtbEjCxPlFTEt8bU3FylRPS4S48OlXi/qyF9P8joyy90pX8q6taZczDRIG/Oa4iXuzCkiXN7dVac3d43pR7RELyKsTU3WcJQwG5eq/IBtaTErdWFpHZK1FypXo8RaicpWCk3dXi2M/ZYWMibrlwguZyNb27K3ClEKn4WRFNpCnh4uiw9tml+LP9DvQLiiQ83RJ3fYAP/2ltgSOx/hNMRbVZYZzYBq0BZ0FmLvUPWz2KJaR28t6jZ9Hw7+PHqga076Hq2kdWWXlHnJber+9N+RFRiJmJXetKzfB5sL35NlTnX60yPLxvemJ/R3P3X7ojn49KTIxZ+P3NfgenEi9PdT9fqgqfM9KHKow0OfY/B756Z1fV42p2p9LXPx5SFXAb3jonG481ceq5h2PhZqZL2Rj88BrcNJBXW9Wvyv/dB8DKf6vHy5jem7tlOPty7bxSoji/5w/TljuPmM5nKO/jzTvHfGW3Lzk35fUOtNpVZvPj599EfNGNC8ZkLmQXnpJN4eRUZeXyq4L+CSIRX/EX9Z4b98eJvTKJOjDiW9T1FOTbfgqemvO1290898ZDJ0ymQqUjNxRINOxG6JPXEHfrZyD7Du6VD53ab8i1j3t7odqD0h66Gz6DJz0KK6mLIfZhetQ/fm/GyZxHiWV57tbUIN7oXvUy2e831A7fGsb7PQt/KvVeRcvy9S0SlEJIu7e2ZeRdCD4s6bzAHpb4oDOksvs1jy5FnfY29Rnp+SEZLrC45FSWciFCbvUkU5clK2v09Yph1ZfavOJlZJrU9uV4/oLiPfjFoYTbdpvg3VeQPc/cCvBMI8xxWIL6guVGsV+g2cjg4cMryg/EREo2Ed4sXfievw97oqu/V2sCTpmEZEUaIz61n1ebS5c5Sa7zevUDZO5wunql1KuQWzh1n9BrdLuci3V43vVuC7lpQNeltvKPofieoMZlZBM1My2bvKA6Gzr1IPGFuH+fiojuanFbymHv2/V4q+Z0m6C7JElPMPaFdxRPQSpZsdkl6e7qzOHt+tkFZ/pyppmvOdZhzok5rVOxOJGnfltkiexuQyRnEJncUvo/hdFl4eXhofWTgqGStJ5vF19NRDlqkHnRNGmhOWQpeVRM3g44trG4v//5HlwtHmjY31GxuPNtdu3lb/b5JPxS/EZ+IqrJVfiZswQg/EoWivXFr5auXmyq2dP+38dedvO3+XTT9ZUZifi8K/nX/+F6CconE=</latexit> Qm(↵) def. = min b, Y Wp(↵, P j bj yj ) <latexit 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<latexit 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  45. Optimal Quantization ↵ = P j bj yj <latexit sha1_base64="J/UT0rKb/egZhQXgBj4nhb0pjSg=">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</latexit>

    <latexit 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<latexit 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<latexit 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quantization <latexit 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sha1_base64="Pv8Yn3B5GzNCGZ4ksVEmu3Zl+xk=">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</latexit> convex <latexit 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<latexit 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<latexit sha1_base64="HL+CWgVEA+ho9MS6+Yq/V1Xlz0w=">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</latexit> non-convex <latexit 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<latexit 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<latexit sha1_base64="VdRImCsKpMsG7hpSphWq5LcEdys=">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</latexit> In general: Qm(↵) ⇠ 1/m1/d. <latexit 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<latexit 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Qm(↵) = <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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min Y max g2Rm R gc(x)(x)d↵(x) + min b P j gjbj <latexit 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sha1_base64="ltLLjI8KzYMVc1XIIjXd55ioYYA=">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</latexit> Qm(↵) def. = min b, Y Wp(↵, P j bj yj ) <latexit 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<latexit 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<latexit sha1_base64="GOtAFge1SPYVu3blkpa6HEvWdms=">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</latexit> g = 0 <latexit 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<latexit 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Lj(0) = V j(Y ) def. = {x ; 8`, ||x yj || 6 ||x y` ||} <latexit 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<latexit 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Voronoi cells: <latexit 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  46. Optimal Quantization ↵ = P j bj yj <latexit sha1_base64="J/UT0rKb/egZhQXgBj4nhb0pjSg=">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</latexit>

    <latexit 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<latexit 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<latexit 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quantization <latexit 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sha1_base64="Pv8Yn3B5GzNCGZ4ksVEmu3Zl+xk=">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</latexit> convex <latexit 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<latexit 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<latexit sha1_base64="HL+CWgVEA+ho9MS6+Yq/V1Xlz0w=">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</latexit> non-convex <latexit 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<latexit 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<latexit sha1_base64="VdRImCsKpMsG7hpSphWq5LcEdys=">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</latexit> In general: Qm(↵) ⇠ 1/m1/d. <latexit 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<latexit 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Qm(↵) = <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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min Y max g2Rm R gc(x)(x)d↵(x) + min b P j gjbj <latexit 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sha1_base64="ltLLjI8KzYMVc1XIIjXd55ioYYA=">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</latexit> Qm(↵) def. = min b, Y Wp(↵, P j bj yj ) <latexit 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<latexit 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<latexit sha1_base64="GOtAFge1SPYVu3blkpa6HEvWdms=">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</latexit> Qm(↵) = min Y Z min 16j6m c(x, yj)d↵(x) <latexit 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<latexit 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<latexit sha1_base64="9+wlP+JAhxLRDNcpaLLF0WoOboo=">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</latexit> Proposition: <latexit 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<latexit 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g = 0 <latexit 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Lj(0) = V j(Y ) def. = {x ; 8`, ||x yj || 6 ||x y` ||} <latexit 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<latexit 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Voronoi cells: <latexit 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  47. Optimal Quantization ↵ = P j bj yj <latexit sha1_base64="J/UT0rKb/egZhQXgBj4nhb0pjSg=">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</latexit>

    <latexit 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<latexit 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<latexit 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quantization <latexit 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sha1_base64="Pv8Yn3B5GzNCGZ4ksVEmu3Zl+xk=">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</latexit> convex <latexit 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<latexit 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<latexit sha1_base64="HL+CWgVEA+ho9MS6+Yq/V1Xlz0w=">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</latexit> non-convex <latexit 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<latexit 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<latexit sha1_base64="VdRImCsKpMsG7hpSphWq5LcEdys=">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</latexit> In general: Qm(↵) ⇠ 1/m1/d. <latexit 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<latexit 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Qm(↵) = <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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min Y max g2Rm R gc(x)(x)d↵(x) + min b P j gjbj <latexit 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sha1_base64="ltLLjI8KzYMVc1XIIjXd55ioYYA=">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</latexit> Qm(↵) def. = min b, Y Wp(↵, P j bj yj ) <latexit 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<latexit 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<latexit sha1_base64="GOtAFge1SPYVu3blkpa6HEvWdms=">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</latexit> Qm(↵) = min Y Z min 16j6m c(x, yj)d↵(x) <latexit 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<latexit 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<latexit sha1_base64="9+wlP+JAhxLRDNcpaLLF0WoOboo=">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</latexit> Proposition: <latexit 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<latexit 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g = 0 <latexit 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Lj(0) = V j(Y ) def. = {x ; 8`, ||x yj || 6 ||x y` ||} <latexit 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<latexit 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Voronoi cells: <latexit 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Local minimizers: <latexit 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<latexit 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<latexit 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<latexit 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<latexit sha1_base64="8E/VHqLSQA66j6RiE/Fgmf7YzZ0=">AABB3HictVzNchu5EYY3f2vnz5vcksskWqe8W44jKVuVVLZStbIky1rTtmxSsneXtmpIjuixhxyaQ8qyuarKIbdUrnmEXJM3yHPkDZJTXiHdDWCAITHTgOIYJQkD4utu9ACN7gbo3iRLi9n6+j8vvfeNb37r2995//KV737v+z/44dUPfnRU5PNpPzns51k+fdKLiyRLx8nhLJ1lyZPJNIlHvSx53Hu5jZ8/Pk2mRZqPO7M3k+TpKB6O05O0H8+g6fjqT7qz5Axwi1bej7NolI7TUfoWAL87P766tn5znf5Fq5UNVVkT6t9B/kF0KLpiIHLRF3MxEokYixnUMxGLAspXYkOsiwm0PRULaJtCLaXPE3EurgB2Dr0S6BFD60v4PYSnr1TrGJ6RZkHoPnDJ4GcKyEhcA0wO/aZQR24RfT4nythaR3tBNFG2N/C3p2iNoHUmnkMrh9M9fXE4lpk4Eb+lMaQwpgm14Oj6isqctIKSR9aoZkBhAm1YH8DnU6j3Can1HBGmoLGjbmP6/F/UE1vxua/6zsW/ScprUCLRVqPPSwqxOCX6Eb3NOXwm5cmA8xAoJGqMWHtNuh7R6MfQfwHt96GcU03rpAdlQa3njchtKC7kNovcg+JC7rHIFhQXssUiD6C4kAcKidgp6dyNb0Nx4dss54dQXMiHLPIRFBfyEYs8guJCHrHIL6G4kF+yyNtQXMjbLPIuFBfyLovsQHEhOyzyEIoLecgid6G4kLsKWb9Sp1ByopMyq3IL6lUeaCkyaNli5btF1tGFveWxpvs1WH5V78BfN3bHQ6dJDXbXY96d1GD5mbcHNtKN5W3RHdpNXNg7LHYfZoAbu89iPxcvarCfe6y0lzVYfq21oJ8by1vfe/Dkxt5jsfeh5sbye9QDaHFjH3jsGJMa7AGLfShe1WB9rP60Bsvb/TbYFTeW36c60N+N9bGm8xosb0+PwINxY/nd6jG0urGPWewTcVaDfcJivwDr7sZ+4bHDvq3B6j32Cu0gQ/JHElixTdTiclVibQLUYoZ/Vu4tGfnGPWjnMMMSMyTMiEXslYg9T0SrRLS85SpKO1qQv8tzaZeItieiV+5NWJux/Qdlf6xlHoidErGzhGjySPFd67GcknehWzjkrNy5sOYzpry031hL1Hxotrwa8aCCkHP7Oc38GxQtYQSFmmqi9rzc4yUyoucmxGuK3vQoNQ8eNyutgo06Y1E9B6rHot44UG9Y1NyBmrOoUwfqlEWZlW/juh4zwOgf38WCnuQMkD5yfYnAK9iCXecOrNEI5s8BeIGPqOUB/G1T7M2VJskwmsd9ErMcTyuWeAq1hViDdhMV7lB8ndEKS0Ay2fOBivHxCXMbC7XmpBU+L3fyqMyY+NNJSZ5hSQe9xYjWUxidu9RyTt6drIXh75TrXtfC8Luk8XPy4mUtDD9T0s8uIHtHYTsXwLZhNU2U9k09lIbMv0gaun6Fdl20uPhWR2rOIL2zQPr76s3sX+C9bFNN6sfUw2gU1viKyvhCaBg9F5aew6ig9yS9Xl2LgkcyVnGvqYfKkNMuOlZymKfQN4N9BurN6HoYjQPwuLYp5l5Y9dDZOylHY+phNI6EzHuekyev62E0hvQs9WHqYTQw2xKrON/UQy07akDGzqYeatXHlAXGHJCc87LFeEVT8pPmilpK/kFztsb2+Vf3MczZPCtjhGZKxretp9Mr97JmibS/kIBVmwXKgf7F3PLBqjQWYpONr6QMs8r+vkrH7PGo+RZoMYLVL88AuJx5BhLqnARa7wwobrBRV3VkGrfJ4nCWnCyhuqp1xnqLhq/MGlXbjqmVi8vMaI0eu2SvC5p7E/IJW6RZTg+t2jdcR5HTUKuiIZ5eiO7eqvVa1f46i5ssISblTOvTiZA8SWuOU11ab1s6vqZOeWZQ5JmPmb+YbT5R1gZjnpxsEcrSxNPup/NIdhvuqzeEyXHLzyJ6o2ivTslqpHQiVbBRqM4WS298Qc+G9iGdySEPSaMP7zFSVCZCnpphFh3z6RFZVNvecrxRXzpDJ+sFWV1tj5vRQws9dKDDY5xt2DHuQ60DMcMhPHU8opwrpa5y0vhU/LI8Hc3pDTZH9FnFQmoa0t4kFQvZFGU/r1B5DWicDTJK96exTEfjuyuU+KjfJY+JXauW/xqd3Orz7ZjmeP1srs/EDIjrJnGNaNXIU135tMxBSrBwfrJJ/mvzKJFfCEe0oRzXZxZnqZcxnfgnFMFOyDPOaLVxq6Pa285PLX+iOR0IfXaOp9k5WciI7F8E+1NOczKiH/vugD5BlxYhIxvpY3fS0rtx+TopO8eMH5cKeavBzLeEbNmc+Gu69uoqaC7KiEHuA+dLc1vrpEW+YEJcp8q6m7XdvPsg0tyTsGeJpGjmynXi/xH91j96nqytzAjUML6BQtk61/vIKWZBHcW0yzfbIN3XlvLDUoZnSmqz/xmZPqxItkMRF8qDu/UAOPfpWfLCWTIluYuVPnIfbcrmIuXJkh5xtCcUxUu7P1Q7MMp9g3bJNVpzXZolQ5gFszKK0H25LPIy32ZeVep+tIv/C3Wj66rWkGIkTAZXaojL7ycUrdlSZjCr5fx9SavJrfXpUq9mPmOaiyNrLX8NrT+D31pu/exHp1exCrdoDkgK5sloRLZEKz38eN2q8NIzU9Myz4afmZO6l91ykfhaWjcTY58GUzmgWXOmsha6fhEaLywaLzx12KGzRqNF3a4t0TEbW3TUaaUvvxBunQDKc5Yy75FpVOohpR1L+VEdsFT5GF+j3rK01llaMaxW+zTAXvM+SPdaX17dX5e7eyRuk2/TJw9Mxi8DWqUp+Vy6tTlSkxSQ8yfKvtqrv0styL1HFhQpy3ucuGLkqVOfynkp6S/UzpaTnTcWQd9beq36aBvbpfqvV5AjWhMFrUuN+IR6JEp+W45oySLdtHyOiDL/MflU0u9ojpnt3uadRBV/wsSbclUZXjJSGJP+uczb/kr0um/FrxHFhHPlXfeAVvgbRgoSozMJbs+yoDeEu5w8SZAebY/s56qdkqd4Y0uimyT1Qvzew8bIqNfMdXtu6RHrsX0MPVHr5q27evD8Mm+OHL+LnOjFtKuNlI+6WHq+GK1Y7XLV5yY9zJf4Gn3MqY8dWZgor4rpik+9uUiJwrhIjA+XsFGEyB8meYjM8nTKl7LurSlXMw3SxjyneIm7B4oIl3d33enNfcSMo7dCr0dYm5ps4ShhNi5X+QHb0mJW6vLKPiRbLzfuRpm1E9XtFJq6vVsY+y0tZELWLxNczkb2tmXvVqIUPgsjKfSFvNFbFx/aND+Fgr8j4YoONUef3GEb/NstsS1238FtiFeqLjOaEbWgLRgsxd6xGme1R7OOXlnUbfo+HPx5pKBrTvqUdtJQ2SVlXnKbuj/912QFpiJhpTc9w8dgc+FHssopZDwpWTZ+NKnQ38UJHYvm4DOSKhd/PvJcgxvFidDfaQobg6bOj6DKIYSHvsfg985N73BeNqdmfa1y8eUhdwF94qJxePJXH6uYfj4Wamq9kXfPAa3DSQN1vVv8r+PQfAyncF6+3Ar6rtkLj7cu+yUqI4v+cPiaMdx8ZnM9R3+eeTk64y25+Um/Lwp6U7k1mndPH/1RMwc0r4WQeVBeOom3Z5GR15cKngu4ZMjFf8Q/LvHfRnhV0qiTI4SSPqeop6Z78NT0Ny5do9Of+chk6NTJVKVm4og23YjdFvviNvxslx5g6O1Q+V1K+Rex7u/PDqD1hKyHzqLLzEGX2hLKfphTtAE9m/uzdRLjXV55t7cDLXgW3qJWvOd7n/rjXd9OZWz13yCRa/2eyMWgEpEsn+6ZddWDEVRP3mQOSH/PN6K79DKLJW+ejTzOFvX9qWWJFvQJf7OgV4vvWVL2aa5O1Fk9nhzgDfu4zA9F4lfUFis7j3sux/mglvPBEueCtFPlcGZ91nw3q47LtsVlUObOTlW/nOJsc57XnBvdqeUi76A344cN+KElZZu0/5Ii4alozubNG2jOlUz2CetY6Eyk1APGmXH5vpsj29MGXqce479bi75rSboHsvQo/x3RCduU6GVKN7skvbzp2JxJvdMgrfoe5fHVtY3l/8tgtXK0eXNj/ebGw821z26p/+fgffFT8XNxHdb4b8RnQO1AHAKHP4i/ir+Jv2892/rj1p+2/iy7vndJYX4sKv+2/vJfui6rzw==</latexit> yj = argmin y Z V j (Y ) c(x, y)d↵(x) <latexit 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<latexit 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  48. Lloyd’s Algorithm Cost c(x, y) = ||x y||2 <latexit sha1_base64="IV+9JenfsXWHPn/R5reZROyRHdk=">AABB3HictVzNchu5EYY3f2vnz5vcksskslN2yqtIylYlVVtbtbIky1rLtmxSsneXtos/I5r2kENzSFkyV1U55JbKNY+Qa/IGeY68QXLKK6R/gAGGxExjFMcoSRgQX3ejB2h0N0B3xskgm66t/fPSB9/69ne++70PL1/5/g9++KMfX/3oJ0dZOpt048NumqSTp512FieDUXw4HUyT+Ol4EreHnSR+0nm9hZ8/OYkn2SAdNadn4/jZsN0fDY4H3fYUml5c/dlWmk2ja90bp7fObn7WGqWT4fz047Pz5xvXXlxdWVtdo3/RcmVdV1aU/neQfhQdqpbqqVR11UwNVaxGagr1RLVVBuVrta7W1Bjanqk5tE2gNqDPY3WurgB2Br1i6NGG1tfwuw9PX+vWETwjzYzQXeCSwM8EkJG6DpgU+k2gjtwi+nxGlLG1jPacaKJsZ/C3o2kNoXWqXkKrhDM9Q3E4lqk6Vr+nMQxgTGNqwdF1NZUZaQUlj5xRTYHCGNqw3oPPJ1DvEtLoOSJMRmNH3bbp839RT2zF567uO1P/JimvQ4lUQ48+zSm01QnRj+htzuAzlicBzn2gEOsxYu0t6XpIox9B/zm0P4ByTjWjkw6UObWeVyK3oPiQWyJyF4oPuSsi96H4kPsi8gCKD3mgkYidkM79+AYUH74hcn4ExYd8JCIfQ/EhH4vIIyg+5JGI/AqKD/mViLwDxYe8IyLvQfEh74nIJhQfsikiD6H4kIcicgeKD7mjkeUrdQIlJToDYVVuQr3IAy1FAi2bony3yTr6sLcD1nS3BCuv6m3468duB+g0LsHuBMy74xKsPPN2wUb6sbItuku7iQ97V8TuwQzwY/dE7BfqVQn2i4CV9roEK6+1fejnx8rW9z48+bH3RewDqPmx8h71EFr82IcBO8a4BHsgYh+pNyXYEKs/KcHKdr8BdsWPlfepJvT3Y0Os6awEK9vTI/Bg/Fh5t3oCrX7sExH7VJ2WYJ+K2C/BuvuxXwbssO9KsGaPvUI7SJ/8kRhWbBW1dr4qsTYGam2Bf5LvLQn5xh1olzD9HNMnzFBE7OaI3UDEfo7YD5Yry+1oRv6uzKWRIxqBiE6+N2FtKvbv5f2xlgQgtnPE9gKiyiPFd23GckLehWmRkNN858JayJjS3H5jLdbzodryGsTDAoLn9kua+bcoWsIICjVVRe1lvsczMqLnKsRbit7MKA0PGTfNrYKLOhVRHQ+qI6LOPKgzETXzoGYi6sSDOhFRduW7uFbADLD6x3cxpyeeAewjl5cIvIJN2HXuwhqNYP4cgBf4mFoewt8Gxd5SqZIMo3ncJzHL8axgiSdQm6sVaLdR4TbF1wmtsBgk454PdYyPT5jbmOs1x1b4PN/JozxjEk5nQPL0czroLUa0nurRuUct5+Tdca0e/m6+7k2tHn6HNH5OXjzX6uGnWvrpBWRvamzzAtgGrKax1r6t16XB+RemYepXaNdFi4tvdajnDNI7rUl/T7+ZvQu8ly2qsX5svR6NzBlfVhhfHRpWz5mj53pU0Htir9fUotojGem419brypDSLjrSctinum8G+/T0mzH1ejQOwOPaoph77tTrzt5xPhpbr0fjSHHe85w8eVOvR6NPz6wPW69HA7MtbR3n23pdy44a4NjZ1uta9RFlgTEHxHOeW6xXNCE/aaapDcg/qM7WuD7/8j6GOZvneYxQTcn6tuV0OvleVi2R8RdisGrTmnKgfzFzfLAijbnaEOMrlmFa2N+X6dg9HjW/D1qMYPXzGYCUM09AQpOTQOudAMV1MeoqjszgNkQczpLjBVRLt05Fb9Hy5axRse0FtUpxmR2t1WOL7HVGc29MPuE+aVbSw37pGy6jKGlov6AhmV4d3b3T67Wo/TURN15AjPOZ1qUTIT5Jq45TfVpvODq+rk95plD4zMfOX8w2H2trgzFPSrYIZani6fYzeSS3DffVW8rmuPmziN4o2qsTshoDOpHKxCjUZIvZG5/Ts6V9SGdyyINpdOE9RprKWPGpGWbRMZ8ekUV17a3EG/VlMnRcz8jqGntcje476L4HXT/G2YId4wHUmhAzHMJTMyDKuZLrKiWNT9TH+eloSm+wOqJPChbS0GB7ExcsZFWU/bJA5S2gcTZwlB5OY5GOwbeWKMlRv08eG7sWLf91Ork159ttmuPls7k8E9MjrhvENaJVw6e6/LTIgSWYez/ZIP+1epTIrw5HtKES1+cOZ9bLiE78Y4pgx+QZJ7TapNVR7O3mpxY/MZwOlDk7x9PslCxkRPYvgv0ppTkZ0Y97d8CcoLNFSMhGhtidQe7d+HydgTjHrB83UHyrwc63mGzZjPgbuu7qymgucsTA+8D5wtw2OtknXzAmrhNt3e3art59EGnvSbizhCnauXKD+N+k3+bHzJOVpRmBGsY3kGlb53sfKcUsqKM27fLVNsj0daW8lsvwXEtt9z8r07WCZNsUcaE8uFv3gHOXnpkXzpIJyZ0t9eF9tCqbi5THC3rE0R5TFM92v693YJT7Fu2SK7TmWjRL+jALpnkUYfpKWeRFvtW8itTDaGf/F+pW10WtIcVI2Qwua0jK78cUrblSJjCref6+ptXk1/pkoVc1nxHNxaGzlr+B1l/AbyO3eQ6j0ylYhds0B5iCfbIa4ZZoqUcYr9sFXmZmGlr22fKzc9L0clsuEl+zdbMx9kltKgc0a0511sLUL0LjlUPjVaAOm3TWaLVo2o0leiHGFk19WhnKrw63Zg3KM5Gy7JEZ1CBASjeWCqPaE6nKMb5BvRNprYm02rBa3dMAd82HIP1rfXF1f5Pv7pG6Q75Nlzwwjl96tEoH5HOZ1upIjSkg50+0fXVXf4takHuHLChS5nucuGL41KlL5TyX9Fd6Z0vJzluLYO4tvdV9jI1tUf23S8ghrYmM1qVBfEI9Yi2/K0e0YJFWHZ8josx/m3wq9juqY2a3t30nUcGfsPEmryrLiyOFEelfyrztLUWve078GlFMONPedQdo1X/DSIExJpPg9ywzekO4y/FJAnu0HbKfy3aKT/FGjkSrJPVcfRZgYzjqtXPdnVtmxGZsv4aeqHX71n09ZH5JMEeJ30VO9Nq0qw21jzpfeL4Yrbbe5YrPVXqYLfC1+phRHzeysFFeEdNSnwZzYYnqcWFMCJd6o6gjfz3J68jMp1OhlE1vQ7mYaWAb85LiJekeKCJ83t0Nrzd3UxhHZ4leh7AuNW6RKGE2LtX5AdfSYlbq8tI+xK2XK3ejxNmJynYKQ93dLaz9ZgsZk/VLlJSz4d6u7K1ClCJnYZhCV/GN3rL40KX5KRT8HSlfdGg4huQOG+DfbqottfMebkO80XXOaEbUgragtxB7t/U4iz2qdfTGoe7SD+EQzmMAupakH9BOWld2pixL7lIPp/+WrMBExaL0tmf9Mbhc5JEsc6ozngFZNnk0A2W+i1N3LIZDyEiKXML58LmGNIpjZb7TVG8Mhro8giKHOjzMPYawd2571+flcqrW1zKXUB68C5gTF4PDk7/yWMX2C7FQE+eNvH8OaB2OK6ib3eJ/HYfhYznV5xXKLaPvmr0KeOvcL9YZWfSH668Zyy1kNpdzDOeZ5qOz3pKfH/t9Ua03lTqjef/00R+1c8DwmivOg8rSMd6dRVbeUCp4LuCTIVX/Uf+4JH8b4U1Oo0yOOpTMOUU5NdNDpma+cekbnfksRCZLp0ymIjUbRzToRuyW2lN34Gcr9wDr3g7l71LyX8T6vz/bg9Zjsh4mi86Zgxa1xZT9sKdoPXq292fLJMa7vHy3twkteBa+T614z/cB9ce7vs3C2Mq/QcJr/b5KVa8QkSye7tl11YERFE/eOAdkvucb0V16zmLxzbNhwNmiuT+1KNGcPpFvFnRK8R1Hyi7N1bE+q8eTA7xh387zQ5H6DbW1tZ3HPVfifFDK+WCBc0baKXI4dT6rvptVxmXL4dLLc2cnul9KcbY9z6vOjW6XcuE76NX4fgW+70jZIO2/pkh4oqqzebMKmjMtk3vCOlImE8l6wDiznb/v6sj2pILXScD475Wi7zmS7oIsHcp/R3TCNiF6idbNDknPNx2rM6l3K6TV36N8cXVlffH/MliuHG2srq+trj/aWPn8tv5/Dj5UP1e/VDdgjf9OfQ7UDtQhcPiD+qv6m/r75vPNP27+afPP3PWDSxrzU1X4t/mX/wIH9Koa</latexit>

    <latexit 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<latexit 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<latexit 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<latexit 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argmin y Z V j ||x y||2d↵(x) = 1 |V j | Z V i xd↵(x) <latexit 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<latexit 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  49. Lloyd algorithm: <latexit sha1_base64="kAe2HeyqZmj4kUmjH8vcYfuKkGE=">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</latexit> <latexit sha1_base64="kAe2HeyqZmj4kUmjH8vcYfuKkGE=">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</latexit> <latexit 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<latexit 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<latexit 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<latexit 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Iter #1 <latexit 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<latexit 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Iter #2 <latexit 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Iter #3 <latexit 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<latexit 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V 4 <latexit 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<latexit 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x3 <latexit 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<latexit 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<latexit 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Lloyd’s Algorithm Cost c(x, y) = ||x y||2 <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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argmin y Z V j ||x y||2d↵(x) = 1 |V j | Z V i xd↵(x) <latexit 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<latexit 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