Random and cyclic projection algorithms for strongly pseudomonotone variational inequalities

Abstract In this paper, we propose a random and cyclic projection algorithm for solving variational inequality problems with special structure where the underlying mapping is strongly pseudomonotone and L -Lipschitz continuous and the constraint set is the intersection of a large number of simple closed convex sets. Compared with some existing incremental constraint projection algorithms, the proposed algorithm has two notable advantages: Its global convergence can be guaranteed under the assumption that F is strongly pseudomonotone, not strongly monotone or monotone plus; It just computes one projection onto a halfspace rather than two or more times projections onto the full or single constraint set at each iteration. Computational experiments are also reported to illustrate the effectiveness of the proposed algorithm.