An Accelerated Three-Term Extension of a Descent Nonlinear Conjugate Gradient Method

Abstract

In an effort to make modification on the classical Polak–Ribière–Polyak method, Wei et al. suggested an efficient nonlinear conjugate gradient method which possesses the sufficient descent property when the line search fulfills the strong Wolfe conditions (by restricting the line search parameters). Here, we develop a three-term extension of the method which satisfies the sufficient descent condition independent of the line search. Also, under a backtracking Armijo-type line search, we establish global convergence of the method without convexity assumption. Using a scalar approximation of the Hessian of the objective function, we suggest an acceleration scheme that can be used in the iterative line search methods of unconstrained optimization. At last, practical merits of the proposed 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.