Semicontinuity of the solution maps to vector equilibrium problems with equilibrium constraints. (4th March 2022)

• Record Type: Journal Article
• Authors: Anh, Lam Quoc
• Is Part Of: Optimization. Volume 71:Number 3(2022)
• Page Start: 737
• Page End: 751
• Publication Date: 2022-03-04
• Subjects: Equilibrium problems with equilibrium constraints -- upper/lower semicontinuity -- level closedness -- generalized convexity; 49J15 -- 49K40 -- 90C31; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1812067
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we are concerned with parametric vector equilibrium problems with equilibrium constraints. We first introduce concepts of generalized semicontinuity and convexity of vector-valued maps in ordered spaces and discuss their properties, as well as their relationships with well-known concepts. Next, employing mentioned concepts of generalized semicontinuity of vector-valued maps, we study sufficient conditions of upper semicontinuity for solution maps to such problems. Then, combining these generalized semicontinuity along with generalized convexity assumptions, sufficient conditions for lower semicontinuity of solution maps to the reference problems are established. Several examples are provided to illustrate the relaxation and essentialness of assumptions. Our results are new, even for special cases of the underlying problems.