The Exactness Property of the Vector Exact l1 Penalty Function Method in Nondifferentiable Invex Multiobjective Programming. (1st December 2016)

• Record Type: Journal Article
• Authors: Antczak, Tadeusz; Studniarski, Marcin
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 12(2016)
• Page Start: 1465
• Page End: 1487
• Publication Date: 2016-12-01
• Subjects: Invex function -- multiobjective programming -- penalized vector optimization problem -- vector exact l1 penalty function -- (weak) Pareto optimal point; 49M30 -- 49J52 -- 90C29 -- 90C30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1233118
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, the vector exact l 1 penalty function method used for solving nonconvex nondifferentiable multiobjective programming problems is analyzed. In this method, the vector penalized optimization problem with the vector exact l 1 penalty function is defined. Conditions are given guaranteeing the equivalence of the sets of (weak) Pareto optimal solutions of the considered nondifferentiable multiobjective programming problem and of the associated vector penalized optimization problem with the vector exact l 1 penalty function. This equivalence is established for nondifferentiable invex vector optimization problems. Some examples of vector optimization problems are presented to illustrate the results established in the article.