A DESCENT FAMILY OF THREE-TERM CONJUGATE GRADIENT METHODS WITH GLOBAL CONVERGENCE FOR GENERAL FUNCTIONS

摘要

In this paper, we introduce a family of three-term conjugate gradient methods for solving unconstrained optimization problems in which the conjugate parameter satisfies a restrictive relation |beta(k)|<= B-k(FR). Also, the sufficient descent property holds when the line search fulfills the strong Wolfe line search. The global convergence of the presented method is proved under the strong Wolfe line search with some mild conditions and even without convexity assumption on the objective function. Numerical experiments are performed on a set of test problems of the CUTEr library, the results of which illustrate the practical effectiveness of this method.