Solving Unconstrained Optimization Problems with Some Three-term Conjugate Gradient Methods

Abstract

In this paper, based on the efficient Conjugate Descent ({\tt CD}) method, two generalized {\tt CD}algorithms are proposed to solve the unconstrained optimization problems.These methods are three-term conjugate gradient methods which the generateddirections by using the conjugate gradient parameters and independent of the line searchsatisfy in the sufficient descent condition. Furthermore, under the strong Wolfe line search,the global convergence of the proposed methods are proved. Also, the preliminary numericalresults on the {\tt CUTEst} collection are presented to show effectiveness of our methods.