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Representation of the polar cone of convex functions and applications

Lachand-Robert, Thomas; Carlier, Guillaume (2008), Representation of the polar cone of convex functions and applications, Journal of Convex Analysis, 15, 3, p. 535-546

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Type
Article accepté pour publication ou publié
Date
2008
Journal name
Journal of Convex Analysis
Volume
15
Number
3
Publisher
Heldermann Verlag
Pages
535-546
Metadata
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Author(s)
Lachand-Robert, Thomas
Carlier, Guillaume
Abstract (EN)
Using a result of Y. Brenier [Comm. Pure Appl. Math. 44 (1991) 375--417] we give a representation of the polar cone of monotone gradient fields in terms of measure-preserving maps, or bistochastic measures. Some applications to variational problems subject to a convexity constraint are given
Subjects / Keywords
Convexity constraint; Euler-Lagrange equation; measure-preserving maps; bistochastic measures