A Family of Hybrid Conjugate Gradient Method with Restart Procedure for Unconstrained Optimizations and Image Restorations

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 modified conjugate gradient method with a single-parameter can be designed. To improve its convergence property and computational efficiency, this conjugate parameter is further improved by using the hybrid technique in its denominator, and meanwhile a restart procedure is set in its search direction. Accordingly, a family of hybrid conjugate gradient method with restart procedure is established in this paper, which is sufficient descent at each iteration without depending onany 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 restoration, all the numerical results show that the new algorithm is effective