广义强非线性拟变分不等式组的迭代算法

Iterative Algorithms for a System of Extended General Strongly Nonlinear Quasi-Variational Inequalities

研究一类新的广义强非线性拟变分不等式组解的存在性及算法.首先建立广义强非线性拟变分不等式组与不动点问题的等价关系.利用这一等价关系讨论广义强非线性拟变分不等式组解的存在性与唯一性.然后给出一个含有误差的投影迭代算法.最后证明了该算法产生的迭代序列收敛到广义强非线性拟变分不等式组的唯一解.

In this paper,we introduce and study a new system of extended general strongly nonlinear quasi-variational inequalities.First,we establish the equivalences between this system and fixed point problems. By using these equivalences,we discuss the existence and uniqueness of solution to the system. And then,we define a new projection iterative algorithm with mixed errors for finding the unique solution of the system. Finally,we prove the convergence of the suggested iterative algorithm.