Abstract: The author presented a class of new conjugate gradient methods with conservative strategy in search direction. The global convergence results of these algorithms were obtained under the condition of general assumptions, and the numerical experiment results of these algorithms were given. The results show that the corresponding algorithms are sufficient descent in the case of the strong Wolfe inexact line search parameters σ<1/4,1/3,1/2, respectively. The new algorithm is suitable for solving largescale unconstrained optimization problems.

Key words: sufficient descent property, global convergence, conjugate gradient method, strong Wolfe inexact line search, unconstrained optimization