A family of accelerated hybrid conjugate gradient method for unconstrained optimization and image restoration

In this paper, a family of hybrid conjugate parameters with restart procedure is proposed. In which, we design a hybrid conjugate parameter by using two hybrid techniques, and set a restart procedure in its search direction according to the conjugate parameter. Under the usual assumptions and the weak Wolfe line search, we prove its sufficient descent property and global convergence. Finally, we choose a specific algorithm from this family and use an acceleration scheme to solve the large-scale unconstrained optimization problems and image restorations. These numerical results show that our algorithm is effective.