Strong Fenchel Duality for Evenly Convex Optimization Problems

Saba Naser Majeed

doi:10.6180/jase.202312_26(12).0004

Strong Fenchel Duality for Evenly Convex Optimization Problems

Mathematics / Statistics

Saba Naser Majeed

Department of Mathematics, College of Education for Pure Sciences Ibn Al-Haitham, University of Baghdad, Baghdad, Iraq

Received: November 10, 2022
Accepted: December 27, 2022
Publication Date: March 23, 2023

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202312_26(12).0004

Among a variety of approaches introduced in the literature to establish duality theory, Fenchel duality was of great importance in convex analysis and optimization. In this paper we establish some conditions to obtain classical strong Fenchel duality for evenly convex optimization problems defined in infinite dimensional spaces. The objective function of the primal problem is a family of (possible) infinite even convex functions. The strong duality conditions we present are based on the consideration of the epigraphs of the c-conjugate of the dual objective functions and the ε-c-subdifferential of the primal objective functions.

Keywords: evenly convex set and function, c-conjugate function, ε - c-subdifferentiability of a function, Fenchel duality

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