Representations of quasi-Newton matrices and their use in limited memory methods

Richard H. Byrd; Jorge Nocedal; Robert B. Schnabel

doi:10.1007/BF01582063

Representations of quasi-Newton matrices and their use in limited memory methods

Richard H. Byrd, Jorge Nocedal^*, Robert B. Schnabel

^*Corresponding author for this work

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-review

403 Scopus citations

Abstract

We derive compact representations of BFGS and symmetric rank-one matrices for optimization. These representations allow us to efficiently implement limited memory methods for large constrained optimization problems. In particular, we discuss how to compute projections of limited memory matrices onto subspaces. We also present a compact representation of the matrices generated by Broyden's update for solving systems of nonlinear equations.

Original language	English (US)
Pages (from-to)	129-156
Number of pages	28
Journal	Mathematical Programming
Volume	63
Issue number	1-3
DOIs	https://doi.org/10.1007/BF01582063
State	Published - Jan 1 1994

Keywords

Quasi-Newton method
constrained optimization
large-scale optimization
limited memory method

ASJC Scopus subject areas

Software
Mathematics(all)

Access to Document

10.1007/BF01582063

Fingerprint Dive into the research topics of 'Representations of quasi-Newton matrices and their use in limited memory methods'. Together they form a unique fingerprint.

Cite this

@article{4f8c8d59922747438c79c7bffbba94f4,

title = "Representations of quasi-Newton matrices and their use in limited memory methods",

abstract = "We derive compact representations of BFGS and symmetric rank-one matrices for optimization. These representations allow us to efficiently implement limited memory methods for large constrained optimization problems. In particular, we discuss how to compute projections of limited memory matrices onto subspaces. We also present a compact representation of the matrices generated by Broyden's update for solving systems of nonlinear equations.",

keywords = "Quasi-Newton method, constrained optimization, large-scale optimization, limited memory method",

author = "Byrd, {Richard H.} and Jorge Nocedal and Schnabel, {Robert B.}",

year = "1994",

month = jan,

day = "1",

doi = "10.1007/BF01582063",

language = "English (US)",

volume = "63",

pages = "129--156",

journal = "Mathematical Programming",

issn = "0025-5610",

publisher = "Springer-Verlag GmbH and Co. KG",

number = "1-3",

}

TY - JOUR

T1 - Representations of quasi-Newton matrices and their use in limited memory methods

AU - Byrd, Richard H.

AU - Nocedal, Jorge

AU - Schnabel, Robert B.

PY - 1994/1/1

Y1 - 1994/1/1

N2 - We derive compact representations of BFGS and symmetric rank-one matrices for optimization. These representations allow us to efficiently implement limited memory methods for large constrained optimization problems. In particular, we discuss how to compute projections of limited memory matrices onto subspaces. We also present a compact representation of the matrices generated by Broyden's update for solving systems of nonlinear equations.

AB - We derive compact representations of BFGS and symmetric rank-one matrices for optimization. These representations allow us to efficiently implement limited memory methods for large constrained optimization problems. In particular, we discuss how to compute projections of limited memory matrices onto subspaces. We also present a compact representation of the matrices generated by Broyden's update for solving systems of nonlinear equations.

KW - Quasi-Newton method

KW - constrained optimization

KW - large-scale optimization

KW - limited memory method

UR - http://www.scopus.com/inward/record.url?scp=0028319529&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028319529&partnerID=8YFLogxK

U2 - 10.1007/BF01582063

DO - 10.1007/BF01582063

M3 - Article

AN - SCOPUS:0028319529

VL - 63

SP - 129

EP - 156

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1-3

ER -

Representations of quasi-Newton matrices and their use in limited memory methods

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this