TY - JOUR
T1 - The Shanno-Toint Procedure for Updating Sparse Symmetric Matrices
AU - Powell, Michael .J.D.
AU - Toint, Philippe
N1 - Copyright 2010 Elsevier B.V., All rights reserved.
PY - 1981/10/1
Y1 - 1981/10/1
N2 - Two recent methods (Shanno, 1978; Toint, 1980) for revising estimates of sparse second derivative matrices in quasi-Newton optimization algorithms reduce to variable metric formulae when there are no sparsity conditions. It is proved that these methods are equivalent. Further, some examples are given to show that the procedure may make the second derivative approximations worse when the objective function is quadratic. Therefore the convergence properties of the procedure are sometimes less good than the convergence properties of other published methods for revising sparse second derivative approximations. © 1981, by Academic Press Inc. (London) Limited.
AB - Two recent methods (Shanno, 1978; Toint, 1980) for revising estimates of sparse second derivative matrices in quasi-Newton optimization algorithms reduce to variable metric formulae when there are no sparsity conditions. It is proved that these methods are equivalent. Further, some examples are given to show that the procedure may make the second derivative approximations worse when the objective function is quadratic. Therefore the convergence properties of the procedure are sometimes less good than the convergence properties of other published methods for revising sparse second derivative approximations. © 1981, by Academic Press Inc. (London) Limited.
UR - http://www.scopus.com/inward/record.url?scp=43949092830&partnerID=8YFLogxK
U2 - 10.1093/imanum/1.4.403
DO - 10.1093/imanum/1.4.403
M3 - Article
VL - 1
SP - 403
EP - 413
JO - IMA Journal of Numerical Analysis
JF - IMA Journal of Numerical Analysis
ER -