Self-adaptive projection algorithms for general variational inequalities

摘要

In this paper, we consider and analyze a new class of self-adaptive projection algorithms for solving general variational inequalities by using the technique of updating the solution. We prove that the convergence of these new methods only requires the pseudomonotonicity, which is a weaker condition than monotonicity. These new methods differ from the previously known splitting methods for solving variational inequalities and related complementarity problems. Proof of convergence is very simple. As special cases, we can obtain a number of four-step forward–backward splitting methods of Noor for solving variational inequalities.