A SELF-ADAPTIVE ITERATIVE ALGORITHM FOR SOLVING THE SPLIT VARIATIONAL INEQUALITY PROBLEM IN HILBERT SPACES

Abstract

The split variational inequality problem (SVIP) was first introduced by Censor et al. Up to now, there is a long list of works concerning algorithms to solve (SVIP). In this paper, we study the split variational inequality problem in Hilbert spaces. In order to solve this problem, we propose a self-adaptive algorithm. Our algorithm uses dynamic step-sizes, chosen based on information of the previous step and their strong convergence is proved. In comparison with the work by Censor et al. (Numer. Algor., 59:301–323, 2012), the new algorithm gives strong convergence results and does not require information about the spectral radius of the operator. And then, we give a numerical experiment to illustrate the performance of our algorithm.