Sizing the BFGS and DFP Updates: A Numerical Study
Abstract
In this study we develop and test a strategy for selectively sizing (multiplying by an appropriate scalar) the approximate Hessian matrix before it is updated in the BFGS and DFP trust-region methods for unconstrained optimization. Our numerical results imply that for use with the DFP update the Oren-Luenberger sizing factor is completely satisfactory and selective sizing is vastly superior to the alternatives of never sizing or first-iteration sizing, and is slightly better than the alternative of always sizing. Numerical experimentation showed that the Oren-Luenberger sizing factor is not a satisfactory sizing factor for use with the BFGS update. Therefore, based on our newly acquired understanding of the situation, we propose a damped Oren-Luenberger sizing factor to be used with the BFGS update. Our numerical experimentation implies that selectively sizing the BFGS update with the damped Oren-Luenberger sizing factor is superior to the alternatives. These results contradict the folk-axiom that sizing should be done only at the first iteration. They also show that without sufficient sizing, DFP is vastly inferior to BFGS; however, when selectively sized, DFP is competitive with BFGS.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1991
- Accession Number
- ADA452254
Entities
People
- M. Contreras
- Richard A. Tapia
Organizations
- Rice University