A projective splitting algorithm for solving generalized mixed variational inequalities

Abstract

Abstract 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 + μk∂f)-1 and never work directly with the operator T +∂f, where μk 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.

Keywords

• projective splitting method
• generalized mixed variational inequality
• pseudomonotonicity