张量变分不等式解的存在性

Existence of Solutions for Tensor Variational Inequalities

用凸分析方法研究张量变分不等式问题解的存在性.首先给出张量变分不等式问题解集为空集的一个必要条件;其次,当张量在集合的退化锥上正定时,证明张量变分不等式问题的解集为非空紧致集,并给出张量变分不等式问题解集为非空紧致集的一些强制性条件及张量变分不等式问题解集为非空紧致集的必要条件.

We investigated the existence of solutions for tensor variational inequality problems by using convex analysis.Firstly,we gave a necessary condition for the solution set of tensor variational inequality problems to be empty.Secondly,when the tensor was positive definite on the asymptotic cone of the set,we proved that the solution set of the tensor variational inequality problems was nonempty and compact,and gave several coercivity conditions for the solution set of tensor variational inequality problems to be nonempty and compact,and gave a necessary condition for the solution set of tensor variational inequality problems to be nonempty and compact.