Continuity of the Solution Mappings for Parametric Generalized Strong Vector Equilibrium Problems  

作　　者：Xianzheng Dong Chi Zhang Lizhi Zhang Xianzheng Dong;Chi Zhang;Lizhi Zhang(Jiangxi V & T College of Communications, Nanchang, China)

机构地区：[1]Jiangxi V & T College of Communications, Nanchang, China

出　　处：《Advances in Pure Mathematics》2021年第12期937-949,共13页理论数学进展（英文）

摘　　要：The stability analysis of the solution mappings for vector equilibrium problems is an important topic in optimization theory and its applications. In this paper, we focus on the continuity of the solution mapping for a parametric generalized strong vector equilibrium problem. By virtue of a nonlinear scalarization technique, a new density result of the solution mapping is obtained. Based on the density result, we give sufficient conditions for the lower semicontinuity and the Hausdorff upper semicontinuity of the solution mapping to the parametric generalized strong vector equilibrium problem. In addition, some examples were given to illustrate that our results improve ones in the literature.The stability analysis of the solution mappings for vector equilibrium problems is an important topic in optimization theory and its applications. In this paper, we focus on the continuity of the solution mapping for a parametric generalized strong vector equilibrium problem. By virtue of a nonlinear scalarization technique, a new density result of the solution mapping is obtained. Based on the density result, we give sufficient conditions for the lower semicontinuity and the Hausdorff upper semicontinuity of the solution mapping to the parametric generalized strong vector equilibrium problem. In addition, some examples were given to illustrate that our results improve ones in the literature.

关 键 词：Parametric Generalized Strong Vector Equilibrium Problem Lower Semicontinuity Hausdorff Upper Semicontinuity Nonlinear Scalarization 

分 类 号：O17[理学—数学]