Banach空间中变分不等式组的广义f-投影迭代算法

The Generalized f-projection Method for a System of Variational Inequalities in Banach Spaces

在Hilbert空间中,利用投影算法的收敛性来研究变分不等式组解的逼近已较广泛.但这个问题在Banach空间的研究却相对较少,主要原因是在Banach空间中投影映射缺少某些良好性质.运用广义f-投影算子,建议和分析了一类计算广义变分不等式组的近似解的迭代算法,在一致光滑和一致凸Banach空间中的一定条件下,建立解的存在性以及由算法生成的迭代序列的强收敛性定理.

In Hilbert spaces, the approximate soluting of a system for variational inequalities has been widely studied. However, relatively little research has been done in Banach spaces, the primary reason is that projection mapping lacks some preferable properties in Banach spaces. In this paper, by using the generalized f-projection operator, iterative algorithm to compute the approximate solutions of the system of generalized variational inequalities is suggested and analyzed in Banach spaces. Under suitable conditions, some exist- ence and strong convergence theorems are established in uniformly smooth and uniformly convex Banach spaces.