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| Volume 4, Number 3, September 2008, pp. 423-432 | |||||||||
| G. Carlier | |||||||||
| Key words: | |||||||||
| Toland's duality, convexity constraint, optimal transportation, DC minimization | |||||||||
| Mathematices Subject Classification: 49K30, 49N15 | |||||||||
|
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| Volume 4, Number 3, September 2008, pp. 423-432 | |||||||||
| G. Carlier | |||||||||
| Key words: | |||||||||
| Toland's duality, convexity constraint, optimal transportation, DC minimization | |||||||||
| Mathematices Subject Classification: 49K30, 49N15 | |||||||||
|
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| Abstract: | |||
| We show that minimizing the difference 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 difference 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. | |||
| Remarks on Toland's duality, convexity constraint and optimal transport | ||