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

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.