Necessary optimality conditions for a semivectorial bilevel problem under a partial calmness condition. (2nd September 2021)

• Record Type: Journal Article
• Authors: Dempe, Stephan; Abderrazzak Gadhi, Nazih; El idrissi, Mohammed; Hamdaoui, Khadija
• Is Part Of: Optimization. Volume 70:Number 9(2021)
• Page Start: 1937
• Page End: 1957
• Publication Date: 2021-09-02
• Subjects: Partial calmness -- limiting subdifferential -- limiting normal cone -- optimality condition -- semivectorial bilevel program; Primary 90C29 -- 90C26 -- 90C46 -- Secondary 49K99; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1763991
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we are concerned with a semivectorial bilevel optimization problem P . Using a partial calmness suitable for bilevel semivectorial problems, we formulate its necessary optimality conditions. Our approach consists of reformulating our problem into a one level optimization problem using successively the k th-objective weighted-constraint and the optimal value reformulation. Our main results are given in terms of the limiting subdifferentials and the limiting normal cones. Completely detailed first-order necessary optimality conditions are then derived in the smooth setting while using the generalized differentiation calculus of Mordukhovich.