A spectral Hestenes–Stiefel CG algorithm for large-scale unconstrained optimization in image restoration problems

Abstract

This paper presents a new method, termed spectral Hestenes-Stiefel conjugate gradient method, for large-scale unconstrained optimization. The generated direction automatically satisfies the sufficient descent property at each iteration, independent of the line searches employed or the convexity of the objective functions. Under standard conditions, the global convergence of the proposed method for general functions can be guaranteed. Numerical experiments are conducted on a set of unconstrained optimization problems with a maximum dimension of 600,000 to assess the effectiveness of the present method. Furthermore, the method is tested on four image restoration problems characterized by varying noise levels. The corresponding numerical results indicate that the encouraging efficiency and promising applicability of the developed method when compared to several existing methods.