An algorithm for generalized variational inequality with pseudomonotone mapping (Q1019789)

A projection algorithm for approximating solutions \(x^*\in C\) (with \(\xi\in F(x^*)\)) of a variational inequality \(\langle\xi,y-x^*\rangle\geq 0, y\in C\) is proposed, where \(F\) is a continuous and pseudomonotone multi-valued mapping from \(C\) into \({\mathbb{R}}^n\) with nonempty compact convex values and \(C\subseteq {\mathbb{R}}^n\) is closed and convex. The authors prove convergence of the algorithm and derive a convergence rate result under additional assumptions on \(F\) and on the solutions set.