An Inexact Alternating Projection Based Prediction-Correction Method for Convex Programming Problem

Abstract

Variational inequality problems have become important tools for studying a wide class problems arising from mathematics and management science. Consequently, designing effective algorithm for solving variational inequality problems is a hot research topic. For a class of variational inequalities, alternating direction method is efficient. when the subproblems can be solved exactly. However, the subproblems could be too difficult or impossible to be solved exactly in many practical applications. In this paper, An inexact alternating direction method based on the prediction-correction method is obtained, At each iteration, one can get a predictor by using projection in alternating fashion, then corrects the predictor to generate the new iterate. And the restrictions on parameters are weakened. A new descent direction and an optimal step size along this descent direction is derived . Convergence of the new method is proved under mild assumptions. Some numerical results demonstrate that our proposed method is efficient and easy to implement.