Abstract

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.

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Keywords

  • Convex optimization
  • saddle-point
  • conjugate duality

Mathematics Subject Classification

46N10, 49J45, 28A35

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Suggested citation

C. Léonard. “Convex Minimization Problems with Weak Constraint Qualifications.” Journal of Convex Analysis 17 (2010), No. 1, 321–348. https://doi.org/10.68381/jca17024

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Published by Heldermann Verlag, 2010. Rights now held by Banach Press LLC.