Projection-type method with line-search process for solving variational inequalities

Abstract

We propose an accelerated projection-type method for solving variational inequalities in Hilbert spaces. The method is suitable for pseudomonotone non-Lipschitz continuous operators and obtains strong convergence for iterative sequences under appropriate conditions. Based on the classical double-projection gradient method, we establish a new line-search rule and add an inertia term to improve the convergence speed of the proposed algorithm. Finally, some numerical examples are implemented to compare the proposed algorithm with the existing results, thereby verifying that our method has better performance.