A New Hybrid HS-DY Conjugate Gradient Method

Conjugate gradient method is one of the most useful methods for solving unconstrained optimization problem. In this paper, we propose a hybrid conjugate gradient method for unconstrained optimization based on the Hestenes-Stiefel and Dai-Yuan conjugate gradient Algorithms. By searching a particular direction, the new algorithm satisfies the descent condition. Furthermore under the Wolfe line search conditions, we prove that the new method can support the global convergence. The initial numerical experiments show that the new algorithm is efficient.