Convergence for vector optimization problems with variable ordering structure. (2nd August 2016)

• Record Type: Journal Article
• Authors: Li, X. B.; Lin, Z.; Peng, Z. Y.
• Is Part Of: Optimization. Volume 65:Number 8(2016)
• Page Start: 1615
• Page End: 1627
• Publication Date: 2016-08-02
• Subjects: Convex vector optimization -- convex set -- Painlevé–Kuratowski convergence -- minimal and efficient point -- perturbation; 49K40 -- 90C29 -- 90C31; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1157879
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we first discuss the Painlevé–Kuratowski set convergence of (weak) minimal point set for a convex set, when the set and the ordering cone are both perturbed. Next, we consider a convex vector optimization problem, and take into account perturbations with respect to the feasible set, the objective function and the ordering cone. For this problem, by assuming that the data of the approximate problems converge to the data of the original problem in the sense of Painlevé–Kuratowski convergence and continuous convergence, we establish the Painlevé–Kuratowski set convergence of (weak) minimal point and (weak) efficient point sets of the approximate problems to the corresponding ones of original problem. We also compare our main theorems with existing results related to the same topic.