Remarks on Toland's duality, convexity constraint and optimal transport
Carlier, Guillaume (2008), Remarks on Toland's duality, convexity constraint and optimal transport, Pacific Journal of Optimization, 4, 3, p. 423-432
TypeArticle accepté pour publication ou publié
Journal namePacific Journal of Optimization
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Abstract (EN)We show that minimizing the di erence of squared Wasserstein distances to two reference probability measures in a suitable set of probability measures is equivalent to a linear programming problem posed on set of convex functions (problem which has its own interest and motivations). This is naturally related to Toland's duality for the minimization of the di erence of convex (DC for short) functions. We therefore end the paper by some remarks on DC problems with a convex (or concave) dual in the sense of Toland.
Subjects / KeywordsToland's duality; convexity constraint; optimal transportation; DC minimization
Showing items related by title and author.
Santambrogio, Filippo; Galichon, Alfred; Carlier, Guillaume (2010) Article accepté pour publication ou publié