An efficient Newton-like conjugate gradient method with restart strategy and its application

Abstract

In an attempt to enhance the theoretical structure of the Hestenes and Stiefel (HS) conjugate gradient method, several modifications of the method are provided, most of which rely on a double-truncated property to analyze its convergence properties. In this paper, a spectral HS method is proposed, which is sufficiently descent and converges globally using Powell’s restart strategy. This modification makes it possible to relax the double bounded property associated with the earlier versions of the HS method. Furthermore, the spectral parameter is motivated by some interesting theoretical features of the generalized conjugacy condition, as well as the quadratic convergence property of the Newton method. Based on some standard test problems, the numerical results reveal the advantages of the method compared to some popular conjugate gradient methods. Additionally, the method also demonstrates reliable results when applied to solve image reconstruction models.