A new extragradient method for generalized variational inequality in Euclidean space

Fixexd point theory and applications

Haibin Chen¹ 

[1] School of Management Science, Qufu Normal University, Rizhao, China

关键词: generalized variational inequalities;    extragradient method;    solution existence;    multi-valued mapping;   

DOI  :  10.1186/1687-1812-2013-139

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we extend the extragradient projection method proposed in (Wang et al. in J. Optim. Theory Appl. 119:167-183, 2003) for the classical variational inequalities to the generalized variational inequalities. For this algorithm, we first prove its expansion property of the generated sequence with respect to the starting point and then show that the existence of the solution to the problem can be verified through the behavior of the generated sequence. The global convergence of the method is also established under mild conditions. MSC:90C30, 15A06.

【 授权许可】

CC BY