Two optimal Dai–Liao conjugate gradient methods

Abstract

Two adaptive choices for the parameter of Dai–Liao conjugate gradient (CG) method are suggested. One of which is obtained by minimizing the distance between search directions of Dai–Liao method and a three-term CG method proposed by Zhang et al. and the other one is obtained by minimizing Frobenius condition number of the search direction matrix. Global convergence analyses are made briefly. Numerical results are reported; they demonstrate effectiveness of the suggested adaptive choices.

Keywords:

• unconstrained optimization
• large-scale optimization
• conjugate gradient method
• condition number
• global convergence

AMS Subject Classifications:

• 65K05
• 49M37
• 65F35

Acknowledgements

The authors are grateful to Professor William W. Hager for providing the CG_Descent code. They also thank the anonymous referees for their valuable comments and suggestions helped to improve the presentation.

Notes

1 This research was supported by Research Councils of Semnan University and Ferdowsi University of Mashhad.