A restart scheme for the memoryless BFGS method

Abstract

Undesirable effects of the direction of the maximum magnification by the scaled memoryless BFGS (Broyden–Fletcher–Goldfarb–Shanno) updating formula are studied, including some probable computational errors as well as weakening the convergence. In light of the insight gained by our analyses, a restart criterion for the method is suggested to accelerate convergence and also to decrease the errors. Convergence analysis of the given method is carried out as well. At last, the efficiency of the proposed restart approach is investigated by numerical tests on a set of CUTEr problems.

Keywords:

• Unconstrained optimization
• restart
• memoryless BFGS method
• maximum magnification

AMS Subject Classifications:

• 90C53
• 65K05
• 65F35

Acknowledgments

The authors owe a major dept of gratitude to Professor Michael Navon for the line search code. They are also thankful to the anonymous reviewer for his/her valuable comments and suggestions that helped to improve the quality of this work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Semnan University.