Stable strong Fenchel and Lagrange duality for evenly convex optimization problems. (1st September 2016)

• Record Type: Journal Article
• Authors: Fajardo, M. D.; Vidal, J.
• Is Part Of: Optimization. Volume 65:Number 9(2016)
• Page Start: 1675
• Page End: 1691
• Publication Date: 2016-09-01
• Subjects: Evenly convex function -- generalized convex conjugation -- Lagrange and Fenchel dual problems; 52A20 -- 26B25 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1167207
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : By means of a conjugation scheme based on generalized convex conjugation theory instead of Fenchel conjugation, we build an alternative dual problem, using the perturbational approach, for a general optimization one defined on a separated locally convex topological space. Conditions guaranteeing strong duality for primal problems which are perturbed by continuous linear functionals and their respective dual problems, which is named stable strong duality, are established. In these conditions, the fact that the perturbation function is evenly convex will play a fundamental role. Stable strong duality will also be studied in particular for Fenchel and Lagrange primal–dual problems, obtaining a characterization for Fenchel case.