Abstract
In this paper, a modified Hestenes–Stiefel conjugate gradient method for unconstrained problems is developed, which can achieves the twin goals of generating sufficient descent direction at each iteration as well as being close to the Newton direction. In our methods, the hybridization parameter can also be obtained based on other kinds of conjugacy conditions. Under mild condition, we establish their global convergence for general objective functions. Numerical experimentation with the new method indicates that it efficiently solves the test problems and therefore is promising.
Acknowledgements
We are sincerely grateful to the anonymous referees and editor for their many constructive and valuable suggestions and comments, which have made the paper clearer and more comprehensive than the earlier version. We would like to thank Professors W.W.Hager and H. Zhang for their CG_DESCENT code for numerical comparison.
Notes
No potential conflict of interest was reported by the authors.