New duality results for evenly convex optimization problems. (2nd September 2021)

• Record Type: Journal Article
• Authors: Fajardo, M. D.; Grad, S. M.; Vidal, J.
• Is Part Of: Optimization. Volume 70:Number 9(2021)
• Page Start: 1837
• Page End: 1858
• Publication Date: 2021-09-02
• Subjects: Evenly convex function -- generalized convex conjugation -- converse duality -- total duality -- Lagrangian function -- convex optimization in locally convex spaces; 52A20 -- 26B25 -- 90C25 -- 49N15; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1756287
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We present new results on optimization problems where the involved functions are evenly convex. By means of a generalized conjugation scheme and the perturbation theory introduced by Rockafellar, we propose an alternative dual problem for a general optimization one defined on a separated locally convex topological space. Sufficient conditions for converse and total duality involving the even convexity of the perturbation function and c -subdifferentials are given. Formulae for the c -subdifferential and biconjugate of the objective function of a general optimization problem are provided, too. We also characterize the total duality by means of the saddle-point theory for a notion of Lagrangian adapted to the considered framework.