Discovery - University of Dundee - Online Publications

Library & Learning Centre

A limited memory steepest descent method

Standard

A limited memory steepest descent method. / Fletcher, Roger.

In: Mathematical Programming, Vol. 135, No. 1-2, 10.2012, p. 413-436.

Research output: Contribution to journalArticle

Harvard

Fletcher, R 2012, 'A limited memory steepest descent method' Mathematical Programming, vol 135, no. 1-2, pp. 413-436., 10.1007/s10107-011-0479-6

APA

Fletcher, R. (2012). A limited memory steepest descent method. Mathematical Programming, 135(1-2), 413-436. 10.1007/s10107-011-0479-6

Vancouver

Fletcher R. A limited memory steepest descent method. Mathematical Programming. 2012 Oct;135(1-2):413-436. Available from: 10.1007/s10107-011-0479-6

Author

Fletcher, Roger / A limited memory steepest descent method.

In: Mathematical Programming, Vol. 135, No. 1-2, 10.2012, p. 413-436.

Research output: Contribution to journalArticle

Bibtex - Download

@article{e90a24eeed7040b3b5a96b36d029086f,
title = "A limited memory steepest descent method",
author = "Roger Fletcher",
year = "2012",
doi = "10.1007/s10107-011-0479-6",
volume = "135",
number = "1-2",
pages = "413--436",
journal = "Mathematical Programming",
issn = "0025-5610",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - A limited memory steepest descent method

A1 - Fletcher,Roger

AU - Fletcher,Roger

PY - 2012/10

Y1 - 2012/10

N2 - The possibilities inherent in steepest descent methods have been considerably amplified by the introduction of the Barzilai-Borwein choice of step-size, and other related ideas. These methods have proved to be competitive with conjugate gradient methods for the minimization of large dimension unconstrained minimization problems. This paper suggests a method which is able to take advantage of the availability of a few additional 'long' vectors of storage to achieve a significant improvement in performance, both for quadratic and non-quadratic objective functions. It makes use of certain Ritz values related to the Lanczos process (Lanczos in J Res Nat Bur Stand 45:255-282, 1950). Some underlying theory is provided, and numerical evidence is set out showing that the new method provides a competitive and more simple alternative to the state of the art l-BFGS limited memory method. © 2011 Springer and Mathematical Optimization Society.

AB - The possibilities inherent in steepest descent methods have been considerably amplified by the introduction of the Barzilai-Borwein choice of step-size, and other related ideas. These methods have proved to be competitive with conjugate gradient methods for the minimization of large dimension unconstrained minimization problems. This paper suggests a method which is able to take advantage of the availability of a few additional 'long' vectors of storage to achieve a significant improvement in performance, both for quadratic and non-quadratic objective functions. It makes use of certain Ritz values related to the Lanczos process (Lanczos in J Res Nat Bur Stand 45:255-282, 1950). Some underlying theory is provided, and numerical evidence is set out showing that the new method provides a competitive and more simple alternative to the state of the art l-BFGS limited memory method. © 2011 Springer and Mathematical Optimization Society.

UR - http://www.scopus.com/inward/record.url?scp=79960458160&partnerID=8YFLogxK

U2 - 10.1007/s10107-011-0479-6

DO - 10.1007/s10107-011-0479-6

M1 - Article

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1-2

VL - 135

SP - 413

EP - 436

ER -

Documents

Library & Learning Centre

Contact | Accessibility | Policy