A variational derivation of a class of BFGS-like methods

ABSTRACT

We provide a maximum entropy derivation of a new family of BFGS-like methods. Similar results are then derived for block BFGS methods. This also yields an independent proof of a result of Fletcher 1991 and its generalization to the block case.

KEYWORDS:

• Quasi-Newton method
• BFGS method
• maximum entropy problem
• block BFGS

Acknowledgments

This paper was written during a stay at the Courant Institute of Mathematical Sciences of the New York University whose hospitality is gratefully acknowledged. In particular, I would like to thank Michael Overton and Esteban Tabak for useful conversations and for pointing out some relevant literature. I would also like to thank Montacer Essid for kindly providing the code and the numerical examples of Section 5.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Michele Pavon http://orcid.org/0000-0002-2648-2445

Additional information

Funding

Supported in part by the Università di Padova Research Project CPDA 140897.