On variational inequalities using directional convexificators. (3rd October 2022)

• Record Type: Journal Article
• Authors: Gadhi, Nazih Abderrazzak
• Is Part Of: Optimization. Volume 71:Number 10(2022)
• Page Start: 2891
• Page End: 2905
• Publication Date: 2022-10-03
• Subjects: Directional convexificators -- continuity directions -- nonsmooth optimization -- variational inequalities -- ∂D∗-convexity; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1888088
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we give some results which constitute an application of directional convexificators recently introduced by Dempe and Pilecka [Necessary optimality conditions for optimistic bilevel programming problems using set-valued programming. J Global Optim. 2015;61:769–788]. After establishing mean value conditions in terms of directional convexificators, we formulate variational inequalities of Stampacchia and Minty type in terms of directional convexificators and use these variational inequalities as a tool to find out necessary and sufficient conditions for a point to be an optimal solution of an inherent optimization problem. An example illustrating our findings is also given.