Set convergence of non-convex vector optimization problem with variable ordering structure. (1st February 2020)

• Record Type: Journal Article
• Authors: Wang, Yu; Li, Xiao-Bing; Liou, Yeong-Cheng
• Is Part Of: Optimization. Volume 69:Number 2(2020)
• Page Start: 329
• Page End: 344
• Publication Date: 2020-02-01
• Subjects: Non-convex vector optimization -- cone-sectionwise connected set -- quasiconnected function -- Kuratowski–Painlevé convergence -- minimal and efficient point; 49K40 -- 90C26 -- 90C29; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1561696
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: The aim of this paper is to establish the convergence of a non-convex vector optimization problem, which is a quasiconnected vector optimization problem with respect to the perturbation of feasible set, objective function and ordering cone. To obtain the convergence results of this problem, we first study the Kuratowski–Painlevé convergence of (weak) minimal point set for a sequence of cone-sectionwise connected sets with variable order structures to that of a given cone-sectionwise connected set, and then investigate the Kuratowski–Painlevé convergence of the sets of (weak) minimal points and (weak) efficient points for perturbed optimization problems to those of a given problem. Several numerical examples are also given to illustrate our main results and compare these results with the corresponding ones of the recent references.