Stability of the set of solutions for generalized vector equilibrium problems with cone constraints. (2nd September 2022)

• Record Type: Journal Article
• Authors: Han, Yu; Huang, Nan-jing
• Is Part Of: Optimization. Volume 71:Number 9(2022)
• Page Start: 2491
• Page End: 2517
• Publication Date: 2022-09-02
• Subjects: Generalized vector equilibrium problem -- cone constraint -- existence of solutions -- upper semicontinuity -- lower semicontinuity; 49J40 -- 49K40 -- 90C31; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1860978
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, the Hausdorff quasi-upper and Hausdorff quasi-lower semicontinuity for set-valued mappings are introduced to derive the upper semicontinuity and lower semicontinuity of cone constraint mapping in normed vector spaces. We discuss existence of solutions for generalized vector equilibrium problems with cone constraints. Moreover, we establish the lower semicontinuity of (weakly) efficient approximate solution mappings, upper semicontinuity of weakly efficient approximate solution mappings, and Hausdorff upper semicontinuity of efficient approximate solution mappings to parametric generalized vector equilibrium problems with cone constraints under some suitable conditions. Some examples are also given to illustrate our main results.