自反巴拿赫空间中混合变分不等式的稳定性与Tikhonov正则化

在自反巴拿赫空间中介绍混合变分不等式的Tikhonov正则化并建立其相关理论.首先,建立Minty型混合变分不等式的解集非空有界的等价刻画.利用Minty型混合变分不等式解集非空有界的等价条件讨论映射与非线性项同时被扰动时,Minty型混合变分不等式的稳定性.基于此稳定性结果,研究Tikhonov正则化的Minty型混合变分不等式解集的特征与扰动分析.进而,获得Tikhonov正则化的广义混合变分不等式解集的特征与扰动分析.

Stability and the Tikhonov regularization theory of mixed variational inequalities in reflexive Banach spaces

This paper aims to introduce the Tikhonov regularization of mixed variational inequalities and establish the corresponding theory in reflexive Banach spaces. Firstly, the equivalence characterization of nonemptiness and boundedness of the solution set of Minty mixed variational inequalities is established. Applying the equivalence characterization, the stability results of Minty mixed variational inequalities are discussed in reflexive Banach spaces, when both the mapping and the nonlinear function are perturbed simultaneously. Based on the stability results, some characterizations and perturbation analysis for the solution sets of the Tikhonov regularized Minty mixed variational inequalities are presented. We further obtain the characterizations and perturbation analysis for the solution sets of the Tikhonov regularized generalized mixed variational inequalities.