On duality for nonconvex minimization problems within the framework of abstract convexity. (3rd April 2022)

• Record Type: Journal Article
• Authors: Bednarczuk, Ewa M.; Syga, Monika
• Is Part Of: Optimization. Volume 71:Number 4(2022)
• Page Start: 949
• Page End: 971
• Publication Date: 2022-04-03
• Subjects: Abstract convexity -- minimax theorem -- Lagrangian duality -- nonconvex optimization -- conjugate duality -- zero duality gap -- Karush–Kuhn–Tucker conditions; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.2010076
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : 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.