Geodesic
Primal Attainment in Convex Infinite Optimization Duality
Journal of convex analysis, Tome 21 (2014) no. 4, pp. 1043-1064.

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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.
Classification : 90C25, 90C48, 49N15
Mots-clés : Convex infinite programming, converse strong duality, minsup duality 
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     author = {M. A. Goberna and M. A. L\'opez and M. Volle},
     title = {Primal {Attainment} in {Convex} {Infinite} {Optimization} {Duality}},
     journal = {Journal of convex analysis},
     pages = {1043--1064},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_4_JCA_2014_21_4_a7/}
}
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M. A. Goberna; M. A. López; M. Volle. Primal Attainment in Convex Infinite Optimization Duality. Journal of convex analysis, Tome 21 (2014) no. 4, pp. 1043-1064. http://geodesic.mathdoc.fr/item/JCA_2014_21_4_JCA_2014_21_4_a7/