参数广义弱向量拟平衡问题解映射的H-连续性刻画  

Characterizations of H-Continuity for Solution Mapping to Parametric Generalized Weak Vector Quasi-Equilibrium Problems

作　　者：邵重阳 彭再云 王泾晶 周大琼 SHAO Chongyang;PENG Zaiyun;WANG Jingjing;ZHOU Daqiong(College of Mathematics and Statistics, Chongqing Jiaotong University,Chongqing 400074, P.R.China)

机构地区：[1]重庆交通大学数学与统计学院,重庆400074

出　　处：《应用数学和力学》2019年第4期452-462,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11431004;11471059);重庆市自然科学基金(cstc2017jcyjAX0382;cstc2018jcyjAX0337);重庆市创新团队(CXTDX201601022);重庆市巴渝学者计划~~

摘　　要：研究了Hausdorff拓扑向量空间中的一类参数广义弱向量拟平衡问题(PGWVQEP)的稳定性.首先,给出了此问题的参数间隙函数,研究了参数间隙函数的连续性.然后,提出了一个与参数间隙函数相关的关键假设,讨论了它的连续性,并给出关键假设的等价刻画.最后,借助于假设,获得了PGWVQEP解映射Hausdorff半连续的充分必要条件.并举例验证了所得结果.The stability of a class of parametric generalized weak vector quasi-equilibrium problems (PGWVQEP) in Hausdorff topological vector spaces, were studied. First, a parametric gap function for the problem was given, and the continuity property of the function was studied. Next, a key hypothesis related to the gap function for the considered problem was presented, the characterizations of this hypothesis were discussed, and an equivalence theorem for the key hypothesis was given. Finally, by means of the hypothesis, the sufficient and necessary conditions for the Hausdorff semicontinuity of the solution mapping to PGWVQEP were obtained. Examples were given to verify the obtained results.

关 键 词：参数广义弱向量拟平衡问题 解映射 参数间隙函数 Hausdorff下半连续 Hausdorff连续 

分 类 号：O224[理学—运筹学与控制论]