A conjugate gradient projection method with restart procedure for solving constraint equations and image restorations

The conjugate gradient projection method is one of the most effective methods for solving large-scale nonlinear monotone convex constrained equations. In this paper, a new search direction with restart procedure is proposed, and a self-adjusting line search criterion is improved, then a three-term conjugate gradient projection method is designed to solve the large-scale nonlinear monotone convex constrained equations and image restorations. Without using the Lipschitz continuity of these equations, the presented method is proved to be globally convergent. Moreover, its R-linear convergence rate is attained under Lipschitz continuity and the usual assumptions. Finally, large-scale numerical experiments for the convex constraint equations and image restorations have been performed, which show that the new method is effective.