A three-term conjugate gradient algorithm for large-scale unconstrained optimization problems

In this paper, a three-term conjugate gradient algorithm is developed for solving large-scale unconstrained optimization problems. The search direction at each iteration of the algorithm is determined by rectifying the steepest descent direction with the difference between the current iterative points and that between the gradients. It is proved that such a direction satisfies the approximate secant condition as well as the conjugacy condition. The strategies of acceleration and restart are incorporated into designing the algorithm to improve its numerical performance. Global convergence of the proposed algorithm is established under two mild assumptions. By implementing the algorithm to solve 75 benchmark test problems available in the literature, the obtained results indicate that the algorithm developed in this paper outperforms the existent similar state-of-the-art algorithms.