Journal of Convex Analysis 21 (2014), No. 4, 1043--1064
Copyright Heldermann Verlag 2014
Primal Attainment in Convex Infinite Optimization Duality
Miguel A. Goberna
Dept. of Statistics and Operations Research, University of Alicante, Apt. de Correos 99, 03080 Alicante, Spain
mgoberna@ua.es
Marco Antonio López
Dept. of Statistics and Operations Research, University of Alicante, Apt. de Correos 99, 03080 Alicante, Spain
marco.antonio@ua.es
Michel Volle
Dép. de Mathématiques, Université d'Avignon, 74 Rue Louis Pasteur, 84029 Avignon, France
michel.volle@univ-avignon.fr
This article provides results guarateeing that the optimal value of a given convex infinite optimization problem and its corresponding surrogate Lagrangian dual coincide and the primal optimal value is attainable. The conditions ensuring converse strong Lagrangian (in short, minsup) duality involve the weakly-inf-(locally) compactness of suitable functions and the linearity or relative closedness of some sets depending on the data. Applications are given to different areas of convex optimization, including an extension of the Clark-Duffin Theorem for ordinary convex programs.
Keywords: Convex infinite programming, converse strong duality, minsup duality.
MSC: 90C25, 90C48, 49N15
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