多项式变分不等式解集的非空紧性和估计

Nonempty compactness and estimation of the solution set for polynomial variational inequalities

针对一类多项式变分不等式问题,首先,利用例外族概念,在多项式函数首项系数张量为正定时,得到解集的非空紧性;然后,在多项式函数是高阶强伪单调的条件下,证明了其解唯一,并给出一个解的估计刻画。

Firstly,for a class of polynomial variational inequality problems with leading positive definite coefficient tensor,the nonempty compactness of the solution set is obtained by using the concept of exceptional family.Secondly,under the condition that the polynomial function is m order strongly pseudo-monotone,the uniqueness of its solution is proved,and an estimation of solutions is also obtained.