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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

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Type
Article accepté pour publication ou publié
Date
2008
Journal name
Pacific Journal of Optimization
Volume
4
Number
3
Publisher
Yokohama Publishers
Pages
423-432
Metadata
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Author(s)
Carlier, Guillaume
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 / Keywords
Toland's duality; convexity constraint; optimal transportation; DC minimization