A Sucient Descent Three-Term Conjugate Gradient Method and its Global Convergence

Abstract

In this paper, we presented a new three-term conjugate gradient method based on combining the conjugate gradient method proposed by Cheng et al [15] with the idea of the modified FR method [22]. In our method, The search directions satisfy the sufficient descent condition independent of the line search. Under some standard assumptions, we establish the global convergence property and the R-linear convergence rate of the proposed method. Numerical results on the standard test problems, in some
well-known library, illustrate computational efficiency of the new method.