Geodesic
Convex Minimization Problems with Weak Constraint Qualifications
Journal of convex analysis, Tome 17 (2010) no. 1, pp. 321-348 Cet article a éte moissonné depuis la source Heldermann Verlag

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One revisits the standard saddle-point method based on conjugate duality for solving convex minimization problems. Our aim is to reduce or remove unnecessary topological restrictions on the constraint set. Dual equalities and characterizations of the minimizers are obtained with weak or without constraint qualifications. The main idea is to work with intrinsic topologies which reflect some geometry of the objective function. The abstract results of this article are applied in other papers to the Monge-Kantorovich optimal transport problem and the minimization of entropy functionals.
Classification : 46N10, 49J45, 28A35
Mots-clés : Convex optimization, saddle-point, conjugate duality 
@article{JCA_2010_17_1_JCA_2010_17_1_a23,
     author = {C. L\'eonard},
     title = {Convex {Minimization} {Problems} with {Weak} {Constraint} {Qualifications}},
     journal = {Journal of convex analysis},
     pages = {321--348},
     year = {2010},
     volume = {17},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2010_17_1_JCA_2010_17_1_a23/}
}
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C. Léonard. Convex Minimization Problems with Weak Constraint Qualifications. Journal of convex analysis, Tome 17 (2010) no. 1, pp. 321-348. http://geodesic.mathdoc.fr/item/JCA_2010_17_1_JCA_2010_17_1_a23/