Strong and total Fenchel dualities for robust composed convex optimization problems in locally convex spaces
Ahmed Rikouane, Mohamed Laghdir, M’hamed Mabrouk– GJM, Volume 9, Issue 1 (2024), 17-39.
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- août 24, 2024
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In this paper, we consider the composed convex optimization problem which consists in minimizing the sum of a convex function and a convex composite function in locally convex Hausdorff topological vector spaces. By using the properties of the epigraph of the conjugate functions, we present some new robust-type constraint qualifications, which completely characterize the strong duality and the stable strong duality. Moreover, some sufficient and/or necessary conditions for the total duality are obtained. We also treat some special cases, rediscovering older results in the literature. At last, the obtained results in this paper are applied to an optimization problem with cone constraints.
Milestones:
Received: August 17, 2023
Accepted: June 28, 2024
Revised: July 02, 2024
Authors:
Ahmed RikouaneDepartment of Mathematics, Faculty of Sciences
B.P. 8106, Agadir, Morocco.
Mohamed Laghdir and M'hamed MabroukDepartement of Mathematics, Faculty of Sciences,
B.P. 20, El-Jadida, Morocco.