广义单调集值混合变分不等式的一类新算法

A New Algorithm for a Class of Generalized Monotone Set-valued Mixed Variational Inequalities

首先证明了广义单调集值混合变分不等式等价于一个新的不动点问题,在此基础上提出了解广义集值混合变分不等式及其相关优化问题的迭代算法,并给出了这类新算法的收敛性分析,我们的结果推广和综合了该领域的一些最新结论。

In this paper, the equivalence between generalized monotone set-valued mixed variational inequalities and a new fixed point problem was established. Based on this equivalence, an iterative method for solving generalized monotone set-valued mixed variational inequalities and the related problems was given. Furthermore convergence analysis of the algorithm was established under the condition of the monotonic property. Our results improve, extend and unify a lot of resent results in this field.