On linear convergence of iterative methods for the variational inequality problem

Abstract

We present new linear convergence results for iterative methods for solving the variational inequality problem. The methods include the extragradient method, the proximal point method, a matrix splitting method and a certain feasible descent method. The proofs of the results are based on certain error bounds related to the algorithmic mappings. Moreover, we show that all these error bounds hold if a projection-type error bound holds.