变分不等式的修正松弛混合最速下降法

The Modified and Relaxed Hybrid Steepest-descent Methods for Variational Inequalities

本文主要研究具有κ-Lipschtz和η强单调性质的经典变分不等式问题,通过几个基本性质和Hilbert空间的性质给出了一类松弛混合最速下降算法,并且证明了该算法的强收敛性。

This paper is the research of the variational inequality with a Lipschitzi and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space. The modified and relaxed hybrid steepest-descent methods is introduced based on some fundamental prop- erties and the properties of the real Hilbert space and the minds of Gauss-Seidel methods. Strong convergence of this method is established under suitable assumptions imposed on the algorithm parameters.