扰动变分不等式的序下半连续性  

Lower Semicontinuity with Set-relations of Perturbed Generalized Vector Quasivational Inequality Problems

作　　者：胡志军[1] 赵素平[2] 

机构地区：[1]广西师范大学数学与统计学院,桂林541004 [2]重庆大学数学与统计学院,重庆401331

出　　处：《重庆理工大学学报（自然科学）》2014年第6期122-125,共4页Journal of Chongqing University of Technology：Natural Science

基　　金：广西教育厅科研立项项目(201106LX047)

摘　　要：对向量优化准则下集值映射(SMVOR)半连续性和集优化准则下集值映射(SMSOR)序半连续性进行了研究。通过举例指出了SMVOR下半连续与SMSOR序下半连续没有关系,在一定条件下由SMVOR上半连续性得到了SMSOR序下半连续。重点讨论了集序关系意义下广义向量拟变分不等式(GVQVI)的序下半连续性。通过对集序关系意义下序下半连续的进一步研究,得到了扰动变分不等式问题的解集在空间上序下半连续的充分条件,并用不同方法证明了该充分条件。The semicontinuity of set-valued mapping under set-valued optimization rules and the lower semicontinuity with set-relations under set optimization rules have been studied. By some examples, one can find the semicontinuity of set-valued mapping under set-valued optimization rules has no rela- tions with the lower semieontinuity with set-relations under set optimization rules. It is easy to get the relation between the upper semicontinuity with the lower semicontinuity with set-relations. In addti- tion, the key point is discussing the lower semicontinuity with set-relations of GVQVI. By analyzing the lower semicontinuity with set-relations, one can conclude the sufficient conditions of the lower semicontinuity with set-relations of perturbed GVQVI and prove the sufficient condition by two differ- ent ways.

关 键 词：集序关系 序下半连续 扰动变分不等式 半连续 

分 类 号：O175.8[理学—数学]