混合变分不等式和非扩张映射解的迭代算法

引入和研究了一类更一般的混合变分不等式,这类混合变分不等式问题包含了许多已知的变分不等式、相补问题等作为特例.利用广义Wiener-Hopf方程技巧给出了一个求解这类混合变分不等式问题解集合和非扩张映射不动点集合公共元素的迭代算法,并在算子是松弛强制和Lipschitzian连续的条件下证明了该算法的收敛性.所得结果可以看作是一种新的和对已有一些结论的推广和改进.

Iterative Methods for Mixed Variational Inequalities and Nonexpansive Mappings

In this paper,we introduce and study a new class of generalized mixed variational inequalities.The class of mixed variational inequalities includes many known variational inequality problems and complementarity problems as special cases.By using the generalized Wiener-Hopf equation technique,we suggest and analyze an iterative method for finding the common element of the set of fixed points of nonexpansive mappings and the set of solutions of the generalized mixed variational inequalities.The strong convergence of the suggested algorithm only requires the relaxed cocoercive and the Lipschitzian continuity of the mappings.Our results can be viewed as a novel and important extension and improvement of the previously known results.