An efficient hybrid conjugate gradient method with sufficient descent property for unconstrained optimization

In order to take advantage of the strong theoretical properties of the FR method and computational efficiency of the PRP+ method, we present a new hybrid conjugate gradient method based on the convex combination of these methods. In our method, the search directions satisfy the sufficient descent condition independent of any line search. Under some standard assumptions, we established global convergence property of our proposed method for general functions. Numerical comparisons on some test problems from the CUTEst library illustrate the efficiency and robustness of our proposed method in practice.