A descent extension of a modified Polak-Ribiere-Polyak method with application in image restoration problem

A one-parameter extension of the modified Polak-Ribiere-Polyak method proposed by Sun and Liu is developed based on the Dai-Liao approach. Two adaptive choices for the parameter of the method are suggested, one of which is obtained by carrying out an eigenvalue analysis, and the other is determined by minimizing the distance between search direction of the method and direction of the three-term conjugate gradient method proposed by Sun and Liu. It is shown that the method may satisfy the sufficient descent condition when its parameter is chosen appropriately. Global convergence analysis is conducted. At last, practical merits of the method are investigated by numerical experiments on a set of CUTEr test functions as well as the well-known image restoration problem. The results show numerical efficiency of the method.