New hybrid conjugate gradient method for unconstrained optimization

In this paper, we propose a new hybrid conjugate gradient method for solving unconstrained optimization problems. The proposed method can be viewed as a convex combination of Liu–Storey method and Dai–Yuan method. An remarkable property is that the search direction of this method not only satisfies the famous D–L conjugacy condition, but also accords with the Newton direction with suitable condition. Furthermore, this property is not dependent on any line searches. Under the strong Wolfe line searches, the global convergence of the proposed method is established. Preliminary numerical results also show that our method is robust and effective.