Hilbert空间中广义变分不等式的近似-似投影算法

在Hilbert空间中研究了广义变分不等式解的近似-似投影算法,该算法包含了近似点算法和似投影算法.首先通过近似算法,获得暂时迭代点,然后利用似投影算法将该暂时的迭代点投影到广义变分不等式的可行集上,获得下一步的迭代点.在集值映象为极大单调的条件下,证明了迭代序列的任意弱聚点都是变分不等式的解.最后,在取特殊的似距离泛函的情况下证明了序列具有唯一的弱聚点.

Proximal Projected-like Method for Solving Generalized Variational Inequalities in Hilbert Spaces

In this paper,we consider the proximal projected-like method for solving generalized variational inequalities in Hilbert spaces.This method includes proximal method and projected-like method.At first,we obtain temporary iteration points by using proximal method,and then by using the projected-like method,we project the temporary point onto the feasible set of generalized variational inequalities to get the next iterative point.Under the assumptions that the set-valued mapping is maximal monotone,we prove that every weak accumulation point of the sequence is a solution of variational inequalities.Finally,under the condition that the distance-like function is a special function,we prove that the sequence has a unique weak accumulation point.