Sufficient optimality conditions and duality results for a bilevel multiobjective optimization problem via a Ψ reformulation. (2nd April 2020)

• Record Type: Journal Article
• Authors: Gadhi, N.; Hamdaoui, K.; El idrissi, M.
• Is Part Of: Optimization. Volume 69:Number 4(2020)
• Page Start: 681
• Page End: 702
• Publication Date: 2020-04-02
• Subjects: Bilevel programming -- convexificator -- duality -- efficient solution -- Ψ-function; Primary 90C29 -- 90C46 -- Secondary 49K99; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1625901
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we are concerned with a bilevel multiobjective optimization problem P . Using the function Ψ introduced by Gadhi and Dempe [Necessary optimality conditions and a new approach to multiobjective bilevel optimization problems. J Optim Theory Appl. 2012;155:100–114], we reformulate P as a single level mathematical programming problem P ∗ and establish/exhibit the global equivalence between the two problems P and P ∗ . Using a generalized convexity introduced by Dutta and Chandra [Convexificator, generalized convexity and vector optimization. Optimization. 2004;53:77–94], we derive sufficient optimality conditions for the problem P and establish Mond-Weir duality results. To illustrate the obtained results some examples are given.