A family of hybrid conjugate gradient method with restart procedure for unconstrained optimizations and image restorations

Abstract

Conjugate gradient method is one of the most effective methods for solving large-scale optimization problems. Based on the CD conjugate parameter and an improved PRP conjugate parameter, a hybrid conjugate parameter with a single-parameter is designed by using two hybrid techniques, and then a restart procedure is set in its search direction to improve its descent property and computational efficiency. Accordingly, a family of hybrid conjugate gradient method with restart procedure is established, which is sufficient descent at each iteration without depending on any selection of line search criterions. Under usual assumptions and using the weak Wolfe line search criterion to generate the steplengths, the global convergence of the proposed family is proved. Finally, choosing a specific algorithm from this family to solve large-scale unconstrained optimization problems and image restorations, all the numerical results show that the proposed algorithm is effective.