广义非线性集值混合拟变分不等式的扰动迭代算法

The Perturbed Iterative Algorithm for Generalized Nonlinear Set-valued Mixed Quasi-variational Inequalities

本文对一类广义非线性集值混合拟变分不等式进行了研究。首先,利用刘理蔚与李育强的结果,可知黄南京的结果中出现的集值映像实际上是单值的。其次,利用Siddiqi和Ansari的方法以及不动点理论,我们证明了这类混合拟变分不等式解的存在性,并给出了一个解这类混合拟变分不等式的新的扰动迭代算法。最后,讨论了这个新的扰动迭代算法的收敛判据。

A class of generalized nonlinear set-valued mixed quasi-variational inequalities is studied in this paper. Firstly, it is shown that the set-valued mapping in the result of Huang is actually single-valued by virtue of the result of Liu and Li. Secondly, the existence of solution for this class of mixed quasi-variational inequalities is proved by the method of Siddiqi and Ansaxi, and a new perturbed iterative algorithm for this class of mixed quasi-variational inequalities is designed. Finally, the convergence criteria for this new perturbed iterative algorithm is discussed.