Banach空间中广义向量均衡问题的适定性  

Well-posedness of Solution for a Generalized Vector Equilibrium Problem

作　　者：赵亚莉 孙若男 张倩[1] 刘鑫[1] ZHAO Ya-li;SUN Ruo-nan;ZHANG Qian;LIU Xin(School of Mathematical Science,Bohai University,Jinzhou 121013,China)

机构地区：[1]渤海大学数学科学学院,辽宁锦州121013

出　　处：《数学的实践与认识》2021年第9期177-187,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11371070);辽宁省教育厅项目(LJ2019011);辽宁省科技厅自然科学基金计划指导项目(2019-ZD-0502)。

摘　　要：主要研究Banach空间中广义向量均衡问题的适定性以及以该广义向量均衡问题为约束的最优化问题的适定性.利用近似解集建立了广义向量均衡问题适定性的度量刻画,而且通过假设近似解集的有界性,给出了广义向量均衡问题广义适定性的充分条件.进一步,证明了以广义向量均衡问题为约束的最优化问题的适定性与广义向量均衡问题适定性之间的关系.所得结果推广了近期文献的某些结果.The well-posedness of solutions for a generalized vector equilibrium problem and optimization problem subject to the generalized vector equilibrium problem is considered in Banach spaces.The metric characterization of the well-posedness for the generalized vector equilibrium problem is established by making use of its approximate solution set and a sufficient condition of the generalized well-posedness for the problem is give.Moreover,The relationship between the well-posedness for the considered optimization problem and that for the generalized vector equilibrium problem is established.The obtained results in this paper extend and generalize the corresponding results in the recent literature.

关 键 词：广义向量均衡问题 广义向量均衡问题为约束的最优化问题 单调性 近似解集 适定性 

分 类 号：O177.2[理学—数学]