TWO DIAGONAL CONJUGATE GRADIENT LIKE METHODS FOR UNCONSTRAINED OPTIMIZATION

In this paper, we studied a two member family of diagonal conjugate gradient like methods for unconstrained minimization problems. The proposed search directions of the methods are obtained by incorporating a diagonal Hessian approximation approach with the modifications of the Polak-Ribiere-Polyak and Liu-Storey parameters. The resulting directions guarantees the sufficient decrease of the objective function free from any line search. The global convergence of the proposed methods using both the Wolfe and Armijotype line search conditions without the convexity assumption on the function is provided. Furthermore, the R-linear convergence rate of the methods are analyzed under Wolfe line search condition. Numerical experiments demonstrated the performance of the method on general unconstrained minimization problems and image restoration problem.