Remarks on toland's duality, convexity constraint and optimal transport

Pacific Journal of Optimization

Volumn 4, Issue 3, 2008, Pages 423-432

  Carlier, G ^a  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Convexity constraint; DC minimization; Optimal transportation; Toland's duality

Indexed keywords

EID: 80054920467     PISSN: 13489151     EISSN: 13498169     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. H. Attouch and M. Théra, A general duality principle for the sum of two operators, J. Convex Anal. 3 (1996) 1-24.
2. Y. Brenier, Polar Factorization and monotone rearrangements of vector valued functions, Communications in Pure and Applied Mathematics, 44 (1991) 375-417.
3. G. Buttazzo, V. Ferone and B. Kawohl, Minimum problems over sets of concave functions and related questions, Math. Nachr. 173 (1995) 71-89.
4. I. Ekeland, Duality in non-convex optimization and calculus of variations, SIAM J. Optim. Control 15 (1977) 905-934.
5. I. Ekeland, Dual variational methods in non-convex optimization and differential equations, in Mathematical Theories of Optimization, Cecconi and Zolezzi (eds.), Springer Lecture Notes in Mathematics 979, 1983.
6. W. Gangbo, An elementary proof of the polar factorization of vector-valued functions, Arch. Rational Mech. Anal. 128 (1994) 380-399.
7. J.-B. Hiriart-Urruty, Generalized differentiability, duality and optimization for problems dealing with differences of convex functions, in Convexity and Duality in Optimization (Groningen, 1984), Lecture Notes in Econom. and Math. Systems, 256, Springer, Berlin, 1985, pp. 37-70.
8. J.F. Toland, Duality in nonconvex optimization, J. Math. Anal. Appl. 66 (1978) 399-415.
9. J.F. Toland, A duality principle for non-convex optimisation and the calculus of variations, Arch. Rational Mech. Anal. 71 (1979) 41-61.
10. J.-C. Rochet and Ph. Choné, Ironing, sweeping and multidimensional screening, Econometrica 66 (1998) 783-826.
11. I. Singer, A Fenchel-Rockafellar type duality theorem for maximization, Bull. Austral. Math. Soc. 20 (1979) 193-198.
12. C. Villani, Topics in Optimal Transportation, Graduate Studies in Mathematics, 58, American Mathematical Society, Providence, RI, 2003.