dfp – Optimization Online

Duality in quasi-newton methods and new variational characterizations of the DFP and BFGS updates

Published: 2007/09/28

Unconstrained Optimization bfgs, dfp, duality, quasi-newton methods, variational problems

It is known that quasi-Newton updates can be characterized by variational means, sometimes in more than one way. This paper has two main goals. We first formulate variational problems appearing in quasi-Newton methods within the space of symmetric matrices. This simplies both their formulations and their subsequent solutions. We then construct, for the first time, … Read more

Variational Problems in Quasi-Newton Methods

Published: 2006/07/18

Osman Guler

Filiz Gurtuna

Olena Shevchenko

Unconstrained Optimization bfgs, dfp, duality, quasi-newton methods, sparse problems, variational problems

It has been known since the early 1970s that the Hessian matrices in quasi-Newton methods can be updated by variational means, in several different ways. The usual formulation of these variational problems uses a coordinate system, and the symmetry of the Hessian matrices are enforced as explicit constraints. As a result, the variational problems seem … Read more