Optimality conditions in terms of convexificators for a bilevel multiobjective optimization problem. (2nd August 2020)

• Record Type: Journal Article
• Authors: Dempe, S.; Gadhi, N.; El idrissi, M.
• Is Part Of: Optimization. Volume 69:Number 7/8(2020)
• Page Start: 1811
• Page End: 1830
• Publication Date: 2020-08-02
• Subjects: Bilevel optimization -- guignard constraint qualification -- convexificators -- optimal value function -- optimality conditions; Primary 90C29 -- 90C26 -- 90C70 -- Secondary 49K99; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1750610
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we are concerned with a multiobjective bilevel optimization problem P, where the lower-level problem is also a multiobjective optimization problem. Using the optimal-value reformulation, together with a scalarization technique, under a nonsmooth generalized Guignard constraint qualification, one gives necessary optimality conditions for the initial problem. As an application, one deduces optimality conditions for a scalar bilevel programming problem in terms of convexificators. An example is given to illustrate our findings.