Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Minimum norm symmetric quasi-Newton updates restricted to subspaces


Author: Robert B. Schnabel
Journal: Math. Comp. 32 (1978), 829-837
MSC: Primary 65K10; Secondary 65F30
DOI: https://doi.org/10.1090/S0025-5718-1978-0492041-X
MathSciNet review: 492041
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The Davidon-Fletcher-Powell and Broyden-Fletcher-Goldfarb-Shanno updates have been the two most successful quasi-Newton updates for a variety of applications. One reason offered in explanation is that they constitute, in an appropriate norm and metric, the minimum norm change to the matrix, or its inverse, being approximated which preserves symmetry and obeys the quasi-Newton equation. Recent methods have reason to consider updates restricted to certain subspaces. In this paper we derive the general minimum norm symmetric quasi-Newton updates restricted to such subspaces. In the same appropriate norm and metric, the minimum norm change update to the matrix or its inverse is shown to be, respectively, the rank-two update which is a particular projection of the DFP or BFGS onto this subspace.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65K10, 65F30

Retrieve articles in all journals with MSC: 65K10, 65F30


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1978-0492041-X
Keywords: Quasi-Newton updates, minimum norm change updates
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society