Strong convergence of extragradient method for generalized variational inequalities in Hilbert space

Journal of inequalities and applications

Haibin Chen¹ 

关键词: generalized variational inequalities;    extra-gradient method;    multi-valued mapping;    maximal monotone mapping;   

DOI  :  10.1186/1029-242X-2014-223

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we present a new type of extra-gradient method for generalized variational inequalities with multi-valued mapping in an infinite-dimensional Hilbert space. For this method, the generated sequence possesses an expansion property with respect to the initial point, and the existence of the solution to the problem can be verified through the behavior of the generated sequence. Furthermore, under mild conditions, we show that the generated sequence of the method strongly converges to the solution of the problem which is closest to the initial point. MSC:90C30, 15A06.

【 授权许可】

CC BY