集值广义强向量拟均衡问题系统解的本质连通区

Essential Connected Components of System Solutions for Set-Valued Generalized Strong Vector Quasi-Equilibrium Problems

摘要: 本文在集值广义强向量拟均衡问题(SVGSVQEP)系统解为通有稳定性的前提下，当约束映射为连续时，目标映射为锥凸的条件下，得到了在构成空间M中集值广义强向量拟均衡问题(SVGSVQEP)系统解至少存在一个本质连通区的结论。由于集值广义强向量拟均衡问题以及变分不等式问题一系列非线性优化问题解的本质连通区都是在单值映射的条件下研究，论文基于这些结论主要修改相关假设条件，将单值映射推广到集值映射，问题解推广到系统解，更进一步得到了集值广义强向量拟均衡问题系统解本质连通区的存在性定理。

Abstract: In this paper, under the premise that the system solution of the set-valued generalized strong vector quasi-equilibrium problem (SVGSVQEP) is universally stable, when the constraint mapping is continuous and the target mapping is cone-convex, we obtain the set-valued generalized strong vector quasi-equilibrium problem in the composition space. There is at least one essential con-nected area in the system solution of the equilibrium problem (SVGSVQEP). Since the existence, stability, and essential connected parts of the solutions to a series of nonlinear optimization problems of set-valued generalized strong vector quasi-equilibrium problems and variational inequalities problems are essentially studied under the condition of single-valued mapping, the paper mainly modifies the relevant assumptions based on these conclusions, and the single-valued mapping is extended to set-valued mapping, the problem solution is extended to the system solution, and the existence theorem of the essential connected region of the system solution of the set-valued generalized strong vector quasi-equilibrium problem is further obtained.