求解Banach空间中变分不等式新的单投影算法

A New Single Projection Algorithm for Solving v-ariational Inequalities in Banach Spaces

本文给出了一个求解2-一致凸的巴拿赫空间中带有Lipschitz连续单调映射的变分不等式问题的算法.我们用自适应步长规则修改了Tseng单投影算法,避免了需要知道相关映射的Lipschitz常数.在一定的假设下,我们建立了该算法在2-一致凸的巴拿赫空间中的强收敛性.我们的结果实际上是把希尔伯特空间中的一些已有的研究成果推广到巴拿赫空间中.

This paper presents an algorithm for solving the problem of variational inequalities with Lipschitz continuous monotone mapping in 2-uniformly convex Banach Spaces.We modified Tseng's single projection algorithm with the adaptive step size rule to avoid the need to know the Lipschitz constant of the correlation mapping.Under certain assumptions,we establish the strong convergence of this algorithm in 2-uniformly convex Banach Spaces.Our result is actually to generalize so-me of the work that has been done in Hilbert space to Banach space.