%0 Journal Article
%T A projective splitting algorithm for solving generalized mixed variational inequalities
%A Xia Fu-quan
%A Zou Yun-zhi
%J Journal of Inequalities and Applications
%D 2011
%I Springer
%X In this paper, a projective splitting method for solving a class of generalized mixed variational inequalities is considered in Hilbert spaces. We investigate a general iterative algorithm, which consists of a splitting proximal point step followed by a suitable orthogonal projection onto a hyperplane. Moreover, in our splitting algorithm, we only use the individual resolvent mapping (I + ¦Ěk f)-1 and never work directly with the operator T + f, where ¦Ěk is a positive real number, T is a set-valued mapping and  f is the sub-differential of function f. We also prove the convergence of the algorithm for the case that T is a pseudomonotone set-valued mapping and f is a non-smooth convex function. 2000 Mathematics Subject Classification: 90C25; 49D45; 49D37.
%K projective splitting method
%K generalized mixed variational inequality
%K pseudomonotonicity
%U http://www.journalofinequalitiesandapplications.com/content/2011/1/27