New Double Projection Algorithm for Solving Variational Inequalities

Abstract EN

We propose a class of new double projection algorithms for solving variational inequality problem, which can be viewed as a framework of the method of Solodov and Svaiter by adopting a class of new hyperplanes.

By the separation property of hyperplane, our method is proved to be globally convergent under very mild assumptions.

In addition, we propose a modified version of our algorithm that finds a solution of variational inequality which is also a fixed point of a given nonexpansive mapping.

If, in addition, a certain local error bound holds, we analyze the convergence rate of the iterative sequence.

Numerical experiments prove that our algorithms are efficient.