On duality for nonconvex minimization problems within the framework of abstract convexity
Ewa M. Bednarczuk, Monika Syga · Optimization · 2021
By applying the perturbation function approach, we propose the Lagrangian and conjugate duals for minimization problems of the sum of two, generally nonconvex, functions. The main tools are the Φ-convexity theory and minimax theorems for Φ-convex functions. We provide conditions ensuring zero duality gap and introduce Φ-Karush–Kuhn–Tucker conditions that characterize solutions to primal and dual problems. We also discuss the relationship between the dual problems introduced in the present investigation and some conjugate-type duals existing in the literature.