Continuity of the solution set mappings for parametric unified weak quasivariational inequalities via free-disposal set mappings. (1st September 2020)

• Record Type: Journal Article
• Authors: Li, Ke-Ke; Peng, Zai-Yun; Lin, Zhi; Long, Xian-Jun
• Is Part Of: Optimization. Volume 69:Number 9(2020)
• Page Start: 1895
• Page End: 1912
• Publication Date: 2020-09-01
• Subjects: Free-disposal set mapping -- nonlinear scalarization -- lower semicontinuity -- out/inner-continuity -- out-openness; 49K40 -- 90C29 -- 90C31; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1684915
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this study, we mainly study the stability for parametric unified weak quasivariational inequality (PUWQVI) under free-disposal set mappings. Firstly, by using a nonlinear scalarization method, we establish the semicontinuity of gap functions and solution mappings for (PUWQVI). Then, under the free-disposal set mapping assumption, we obtain some sufficient conditions of the outer-continuity and the outer-openness for (PUWQVI), and the inner-openness for parametric unified set-valued strong vector quasivariational inequality, respectively. Moreover, examples are given to illustrate our results, our results are new and improve the corresponding ones in the literature.