Two families of self-adjusting spectral hybrid DL conjugate gradient methods and applications in image denoising

Abstract

The study in this paper introduces two families of self-adjusting spectral hybrid DL conjugate gradient methods to solve unconstrained optimization problems. The search directions in the proposed methods are improved by integrating the negative spectral gradient and the last search direction that has convex combination structure. One component of composite conjugate parameter in the search direction is a hybridization of DL-like conjugate parameter and another flexible conjugate parameter. It is proved that the search directions in the two families of newly proposed methods always automatically satisfy the sufficient descent property, which is independent of choosing the specific conjugate parameter and line search. With general nonconvex objective functions, the convergence results under the weak Wolfe line search are obtained. Numerical experiments verify the efficiency and applicability of our developed methods by comparison with some existing methods for solving unconstrained optimization and image restoration problems.