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
<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).
<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).