On duality for nonconvex minimization problems within the framework of abstract convexity

Abstract: By applying the perturbation function approach, we propose the Lagrangian and the conjugate duals for minimization problems of the sum of two, generally nonconvex, functions. The main tool is the abstract convexity theory, called $\Phi$-convexity, and minimax theorems for Φ\Phi-convex functions. We provide conditions ensuring zero duality gap and introduce generalized Karush-Kuhn-Tucker conditions that characterize solutions to primal and dual problems. We also discuss the relationship between the dual problems proposed the present investigation and some conjugate-type duals existing in the literature. The presentation is based on joint works with Monika Syga.

optimization and control

Audience: researchers in the topic

Variational Analysis and Optimisation Webinar

Series comments: Register on www.mocao.org/va-webinar/ to receive information about the zoom connection.