HS-LS-CD Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization

Conjugate gradient methods are important for large-scale unconstrained optimization. In this paper, we propose anew formula ß_k for unconstrained optimization, which is the hybrid from HS method, LS method and CD method. From the construction of the new formula ß_k, we use a direction which is different from traditional d_k. The direction satisfies descent conditions naturally. And d_k ^Tg_k=-¿g_k¿² depends neither on the line search used nor on the convexity of the objective function. Under suitable conditions, we prove that the new method can ensure the global convergence. Numerical experiments show that the algorithm is efficient.