A New Derivation of Symmetric Positive Definite Secant Updates.
Abstract
In this paper, we introduce a simple new set of techiques for deriving symmetric and positive definite secant updates. We use these techniques to present a simple new derivation of the BFGS update using neither matrix inverses nor weighting matrices. A related derivation is shown to generate a large class of symmetric rank-two update formulas, together with the condition for each to preserve positive definiteness. We apply our techniques to generate a new projected BFGS update, and indicate applications to the efficient implementation of secant algorithms via the Cholsky factorization. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1980
- Accession Number
- ADA093060
Entities
People
- J. E. Dennis Jr.
- Robert B. Schnabel
Organizations
- University of Colorado Boulder