A New Dai-Liao Conjugate Gradient Method based on Approximately Optimal Stepsize for Unconstrained Optimization

Abstract

Conjugate gradient methods are a class of very effective iterative methods for large-scale unconstrained optimization. In this paper, a new Dai-Liao conjugate gradient method for solving large-scale unconstrained optimization problem is proposed. Based on the approximately optimal stepsize for the gradient method, we derive three new choices for the important parameters t_k in Dai-Liao conjugate gradient method. The search direction satisfies the sufficient descent condition, and the global convergences of the proposed method for uniformly convex and general functions are proved under some mild conditions. Numerical experiments on a set of test problems from the CUTEst library show that the proposed method is superior to some well-known conjugate gradient methods.

Keywords:

• Conjugate gradient method
• Dai-Liao conjugate parameter
• global convergence
• the approximately optimal stepsize

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 90C06
• 65K

Acknowledgments

We would like to thank the associate editor and the anonymous referees for their valuable comments and suggestions. We also would like to thank Professors W. W. Hager and H. C. Zhang for their C code of CG DESCENT, and thank Professor Y. H. Dai and Dr. C. X. Kou for their C code of CGOPT (1.0).

Additional information

Funding

The research was supported by National Science Foundation of China (No.12261019), Guizhou Provincial Science and Technology Projects (No. QHKJC-ZK[2022]YB084).