Operator-Splitting Methods for General Mixed Variational Inequalities

摘要

In this paper, we use the technique of updating the solution to suggest and analyze a class of new splitting methods for solving general variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Our method includes the two-step forward-backward splitting and extragradient methods for solving various classes of variational inequalities and complementarity problems as special cases.