Strong convergence of extragradient method for generalized variational inequalities in Hilbert space
Haibin Chen, Yiju Wang, Gang Wang · Journal of Inequalities and Applications · 2014
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.