A Nonmonotone Scaled Fletcher-Reeves Conjugate Gradient Method with Application in Image Reconstruction

In an effort to make modification on the classical Fletcher-Reeves method, Jiang and Jian suggested an efficient nonlinear conjugate gradient algorithm which possesses the sufficient descent property when the line search fulfills the strong Wolfe conditions. Here, we develop a scaled modified version of the method which satisfies the sufficient descent condition independent of the line search. Also, a nonmonotone backtracking Armijo-type line search is proposed under which the global convergence of the method is established without convexity assumption. Performance of the method is evaluated by computational experiments on a set of CUTEr test functions and also, on the image reconstruction as a case study. The results show numerical efficiency of the method.