Characterization of (weakly/properly/robust) efficient solutions in nonsmooth semi-infinite multiobjective optimization using convexificators. (1st February 2018)

• Record Type: Journal Article
• Authors: Kabgani, Alireza; Soleimani-damaneh, Majid
• Is Part Of: Optimization. Volume 67:Number 2(2018)
• Page Start: 217
• Page End: 235
• Publication Date: 2018-02-01
• Subjects: Nonsmooth optimization -- multiobjective optimization -- convexificator -- semi-infinite programming -- constraint qualification; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1393675
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: The main aim of this paper is to investigate weakly/properly/robust efficient solutions of a nonsmooth semi-infinite multiobjective programming problem, in terms of convexificators. In some of the results, we assume the feasible set to be locally star-shaped. The appearing functions are not necessarily smooth/locally Lipschitz/convex. First, constraint qualifications and the normal cone to the feasible set are studied. Then, as a major part of the paper, various necessary and sufficient optimality conditions for solutions of the problem under consideration are presented. The paper is closed by a linear approximation problem to detect the solutions and by studying a gap function.