A three-term conjugate gradient algorithm with restart procedure to solve image restoration problems

Based on the Liu–Storey conjugate gradient method, a three-term conjugate gradient method with restart procedure is proposed for unconstrained optimization. The designed restart condition is chosen according to the Liu–Storey conjugate parameter, and the restart direction consists of the first and third items in the non-restart direction, which can be picked flexibly. Without depending on any line search, the resulting direction satisfies the sufficient descent condition. Moreover, the proposed method possesses the global convergence under usual assumptions and the weak Wolfe line search. Finally, medium–large-scale numerical experiments are conducted for solving unconstrained optimization and image restoration problems, and the numerical results show that the proposed method is promising and practical, even compared with the state-of-the-art methods.