Necessary and Sufficient Conditions for Weak Quasi Efficiency in Nonsmooth Multiobjective Problems. (3rd June 2017)

• Record Type: Journal Article
• Authors: Golestani, M.; Sadeghi, H.; Tavan, Y.
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 6(2017)
• Page Start: 683
• Page End: 704
• Publication Date: 2017-06-03
• Subjects: Constraint qualification -- duality -- Kuhn-Tucker vector critical points -- nonsmooth multiobjective problems -- weak quasi efficient point; 90C30 -- 90C46 -- 49J52 -- 90C29 -- 49J40; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1261155
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, a multiobjective problem with a feasible set defined by inequality, equality and set constraints is considered, where the objective and constraint functions are locally Lipschitz. Several constraint qualifications are given and the relations between them are analyzed. We establish Kuhn-Tucker and strong Kuhn-Tucker necessary optimality conditions for (weak) quasi efficiency in terms of the Clarke subdifferential. By using two new classes of generalized convex functions, sufficient conditions for local (weak) quasi efficient are also provided. Furthermore, we study the Mond-Weir type dual problem and establish weak, strong and converse duality results.