Abstract: In order to effectively solve the large-scale unconstrained optimization problem, based on the trust region technique and the modified quasi-Newton equation, a new non-monotone conjugate gradient algorithm is presented by combining Zhang H. C. and Gu N. Z. strategy in this paper. The trust region technique is applied to ensure the robustness and convergence of the algorithm, and the global convergence property of the algorithm is also analyzed. Under some reasonable conditions, it is proved that the proposed algorithm is linear convergent. Numerical examples indicate that the new algorithm can effectively solve ill-conditioned and large-scale problems. Compared with the algorithm that combines one of the non-monotonic strategies, the new algorithm requires fewer iteration numbers and less running time, and the function value obtained by the new algorithm is closer to the optimal value.

Key words: conjugate gradient algorithm, non-monotone strategy, global convergence, convergence speed