Necessary optimality conditions for a bilevel multiobjective programming problem via a Ψ-reformulation. (2nd December 2018)

• Record Type: Journal Article
• Authors: Lafhim, L.; Gadhi, N.; Hamdaoui, K.; Rahou, F.
• Is Part Of: Optimization. Volume 67:Number 12(2018)
• Page Start: 2179
• Page End: 2189
• Publication Date: 2018-12-02
• Subjects: Multiobjective optimization -- local weak efficient solution -- optimality conditions -- Ψ-function -- bilevel programming; 90C26 -- 90C29 -- 90C30 -- 90K46; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1523402
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we are concerned with a bilevel multiobjective optimization problem . First, using Ψ, a function introduced by Gadhi and Dempe [Necessary optimality conditions and a new approach tomulti-objective bilevel optimization problems. J Optim Theory Appl. 2012;155:100–114], we transform into a one level optimization problem . Second, on terms of convexificators, using a scalarization technique, we derive a Karash-Kuhn-Tucker (KKT)-type necessary optimality conditions to the initial problem under a generalized Abadie constraint qualification without the assumption that the lower-level problem satisfies the Mangasarian Fromovitz constraint qualification. Some examples have been introduced to illustrate our results.