Strong Fenchel Duality for Evenly Convex Optimization Problems

Abstract

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