A new family of hybrid conjugate gradient method for unconstrained optimization and its application to regression analysis

Abstract

We know many conjugate gradient algorithms (CG) for solving unconstrained optimization problems. In this paper, based on the three famous Liu–Storey (LS), Fletcher–Reeves (FR) and Polak–Ribiére–Polyak (PRP) conjugate gradient methods, a new hybrid CG method is proposed. Furthermore, the search direction satisfies the sufficient descent condition independent of the line search. Likewise, we prove, under the strong Wolfe line search, the global convergence of the new method. In this respect, numerical experiments are performed and reported, which show that the proposed method is efficient and promising. In virtue of this, the application of the proposed method for solving regression models of COVID-19 is provided.