Optimality Conditions for a Nonsmooth Semivectorial Bilevel Optimization Problem. (17th February 2021)

• Record Type: Journal Article
• Authors: Dempe, S.; Gadhi, N.; El Idrissi, M.
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 3(2021)
• Page Start: 298
• Page End: 319
• Publication Date: 2021-02-17
• Subjects: Calm -- constraint qualification -- limiting subdifferential -- limiting normal cone -- optimality condition -- semivectorial bilevel program; Primary 90C29 -- 90C26 -- 90C70 -- Secondary 49K99; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1875484
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we are concerned with a nonsmooth semivectorial bilevel optimization problem ( P ). Using a scalarization technique, we transform the lower-level problem into several scalar optimization problems ( P z x s ) . We give necessary optimality condition in terms of the limiting subdifferentials and the limiting normal cones. Completely detailed first-order necessary optimality conditions are then derived in the special case where all functions are strictly differentiable.