AN IMPLICIT METHOD FOR SOLVING NONCONVEX VARIATIONAL INEQUALITIES

Abstract

This paper presents a predictor-corrector algorithm for solving the strongly nonlinear general noncovex variational inequality, which is a class of nonconvex variational inequalities involving three nonlinear operators.  We establish the equivalence between the strongly nonlinear general nonconvex variational inequalities and the fixed point problem, and show that the convergence of the predictor-corrector method only requires pseudomonotonicity, which is a weaker condition than monotonicity.  Some special cases are also discussed.