Article citationsMore>>

Xu, X. and Xu, Y.D. (2019) Connectedness and Path Connectedness of Weak Efficient Solution Sets of Vector Optimization Problems via Nonlinear Scalarization Methods. Mathematics, 7, 947-956.
https://doi.org/10.3390/math7100947

has been cited by the following article:

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

  AUTHORS: Xianzheng Dong, Chi Zhang, Lizhi Zhang

  KEYWORDS: Parametric Generalized Strong Vector Equilibrium Problem, Lower Semicontinuity, Hausdorff Upper Semicontinuity, Nonlinear Scalarization

  JOURNAL NAME: Advances in Pure Mathematics, Vol.11 No.12, December 16, 2021

  ABSTRACT: 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.