First- and second-order optimality conditions in optimistic bilevel set-valued programming. (3rd July 2022)

• Record Type: Journal Article
• Authors: Lafhim, Lahoussine
• Is Part Of: Optimization. Volume 71:Number 7(2022)
• Page Start: 1955
• Page End: 1981
• Publication Date: 2022-07-03
• Subjects: Bilevel optimization -- first- and second-order approximations -- optimality conditions -- set-valued optimization; Primary: 90C29 -- 90C26 -- 90C70 -- Secondary:49K99; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1846189
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this work we adapt the main results from Khanh and Tung [First and second-order optimality conditions without differentiability in multivalued vector optimization. Positivity. 2015;19:817–841] for a general set-valued optimization problem to an optimistic bilevel set-valued programming problem as an optimization problem with implicitly given set-valued constraints. Using the optimal value function, we convert our problem into a one level set-valued optimization problem with general inequality constraints and derive both necessary conditions and sufficient conditions of order one and two. The main tools we exploit are approximations of set-valued mappings. To illustrate the obtained results, some examples are given.