Optimality conditions of a set valued optimization problem with the help of directional convexificators. (4th March 2021)

• Record Type: Journal Article
• Authors: Gadhi, Nazih Abderrazzak; Rahou, Fatima Zahra; El idrissi, Mohammed; Lafhim, Lahoussine
• Is Part Of: Optimization. Volume 70:Number 3(2021)
• Page Start: 575
• Page End: 590
• Publication Date: 2021-03-04
• Subjects: Directional convexificators -- optimality conditions -- set valued optimization -- scalarization -- support function; Primary 90C29 -- 90C46 -- Secondary49K99; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1725512
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: Motivated by a work of Dempe and Pilecka [Necessary optimality conditions for optimistic bilevel programming problems using set-valued programming. J Global Optim. 2015;61:769–788], where the authors introduced the notion of directional convexificators, we investigate a set valued optimization problem P . Using a scalarization technique by mean of the Hiriart-Urruty signed distance function, together with directional convexificators, we give necessary optimality conditions of ( P ) . Sufficient optimality conditions are obtained under a new generalized convexity. To illustrate the obtained results, an example is given.