The Hager–Zhang conjugate gradient algorithm for large-scale nonlinear equations

ABSTRACT

In this paper, the Hager–Zhang (HZ) conjugate gradient (CG) algorithm is studied for large-scale smooth optimization problems. (i) Some results of the HZ CG method for smooth unconstrained optimization problems are given, and a modified HZ (MHZ) CG method is proposed; (ii) the HZ and MHZ CG methods for nonlinear equations are analysed, the global convergence is established and numerical results for large-scale nonlinear equation problems are reported (1,00,000 variables).

Keywords:

• Optimization
• nonlinear equations
• large-scale
• conjugate gradient
• global convergence

2010 AMS SUBJECT CLASSIFICATION:

• 90C26

Acknowledgments

The authors thank the editor, Dr. Suguna Selvakumar, and the referees for their helpful comments that greatly improved this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Zhou Sheng http://orcid.org/0000-0001-9295-5872

Additional information

Funding

This work is supported by the Guangxi Science Fund for Distinguished Young Scholars [grant number 2015GXNSFGA139001] and China NSF – National Natural Science Foundation of China [grant numbers 11261006 and 11661009].