Solving quasimonotone and non-monotone variational inequalities

Abstract

We present a simple iterative method for solving quasimonotone as well as classical variational inequalities without monotonicity. Strong convergence analysis is given under mild conditions and thus generalize the few existing results that only present weak convergence methods under restrictive assumptions. We give finite and infinite dimensional numerical examples to compare and illustrate the simplicity and computational advantages of the proposed scheme.