一类集值混合变分不等式的自适应投影算法与收敛性

Adaptive Projection Algorithm and Convergence of A Class of Set-valued Mixed Variational Inequalities

给出求解一类集值混合变分不等式的自适应投影算法。在算法的步骤中引入含非线性泛函g的邻近算子并改进步长,在一定条件下,证明该算法的强收敛性。在特殊情形下,算法即为通常集值变分不等式的自适应投影算法,因而推广相关结果。

An adaptive projection algorithm for solving a class of set-valued mixed variational inequalities is presented in this paper.In the step of the algorithm,a neighboring operator with nonlinear functional is introduced and the step size is improved.In the special case,the algorithm in this paper is the adaptive projection algorithm of the usual set-valued variational inequalities.The results of previous scholars are generalized.