Large-Scale Quasi-Newton Trust-Region Methods With Low-Dimensional Linear Equality Constraints

Brust, Johannes J.; Marcia, Roummel F.; Petra, Cosmin G.

doi:10.1007/s10589-019-00127-4

Title: Large-Scale Quasi-Newton Trust-Region Methods With Low-Dimensional Linear Equality Constraints

Abstract

We propose two limited-memory BFGS (L-BFGS) trust-region methods for large-scale optimization with linear equality constraints. Here, the methods are intended for problems where the number of equality constraints is small. By exploiting the structure of the quasi-Newton compact representation, both proposed methods solve the trust-region subproblems nearly exactly, even for large problems. We derive theoretical global convergence results of the proposed algorithms, and compare their numerical effectiveness and performance on a variety of large-scale problems.

Authors:

^[1]; Marcia, Roummel F. ^[2]; Petra, Cosmin G. ^[3]

Argonne National Lab. (ANL), Argonne, IL (United States)
Univ. of California, Merced, CA (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:: 2019-09-05

Research Org.:: Argonne National Lab. (ANL), Argonne, IL (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1596681

Alternate Identifier(s):: OSTI ID: 1575872

Report Number(s):: LLNL-JRNL-755231
Journal ID: ISSN 0926-6003; 154974

Grant/Contract Number:: AC02-06CH11357; AC52-07NA27344

Resource Type:: Accepted Manuscript

Journal Name:: Computational Optimization and Applications

Additional Journal Information:: Journal Volume: 74; Journal Issue: 3; Journal ID: ISSN 0926-6003

Publisher:: Springer

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; L-BFGS; Compact Representation; Eigendecomposition; Linear Equality Constraints; Quasi-Newton; Shape-Changing Norm; Trust-Region Algorithm; Linear equality constraints; Trust-region algorithm; Compact representation; Shape-changing norm

Citation Formats


                    Brust, Johannes J., Marcia, Roummel F., and Petra, Cosmin G. Large-Scale Quasi-Newton Trust-Region Methods With Low-Dimensional Linear Equality Constraints.  United States: N. p., 2019. 
Web.  doi:10.1007/s10589-019-00127-4.

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                    Brust, Johannes J., Marcia, Roummel F., & Petra, Cosmin G. Large-Scale Quasi-Newton Trust-Region Methods With Low-Dimensional Linear Equality Constraints.  United States.  https://doi.org/10.1007/s10589-019-00127-4

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                    Brust, Johannes J., Marcia, Roummel F., and Petra, Cosmin G. Thu .  
"Large-Scale Quasi-Newton Trust-Region Methods With Low-Dimensional Linear Equality Constraints".  United States.  https://doi.org/10.1007/s10589-019-00127-4.  https://www.osti.gov/servlets/purl/1596681.

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@article{osti_1596681,

  title        = {Large-Scale Quasi-Newton Trust-Region Methods With Low-Dimensional Linear Equality Constraints},

  author       = {Brust, Johannes J. and Marcia, Roummel F. and Petra, Cosmin G.},

  abstractNote = {We propose two limited-memory BFGS (L-BFGS) trust-region methods for large-scale optimization with linear equality constraints. Here, the methods are intended for problems where the number of equality constraints is small. By exploiting the structure of the quasi-Newton compact representation, both proposed methods solve the trust-region subproblems nearly exactly, even for large problems. We derive theoretical global convergence results of the proposed algorithms, and compare their numerical effectiveness and performance on a variety of large-scale problems.},

  doi          = {10.1007/s10589-019-00127-4},

  journal      = {Computational Optimization and Applications},

  number       = 3,

  volume       = 74,

  place        = {United States},

  year         = {2019},

  month        = {9}

}

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Works referenced in this record:

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Moré, Jorge J.; Sorensen, D. C.
SIAM Journal on Scientific and Statistical Computing, Vol. 4, Issue 3
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Byrd, Richard H.; Nocedal, Jorge; Schnabel, Robert B.
Mathematical Programming, Vol. 63, Issue 1-3
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Byrd, Richard H.; Gilbert, Jean Charles; Nocedal, Jorge
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A trust region algorithm for equality constrained optimization
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Powell, M. J. D.; Yuan, Y.
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Compact representation of the full Broyden class of quasi-Newton updates: Compact Representation of the Full Broyden Class of Quasi-Newton Updates
journal, May 2018

DeGuchy, Omar; Erway, Jennifer B.; Marcia, Roummel F.
Numerical Linear Algebra with Applications, Vol. 25, Issue 5
DOI: 10.1002/nla.2186

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journal, August 1998

Lalee, Marucha; Nocedal, Jorge; Plantenga, Todd
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On efficiently combining limited-memory and trust-region techniques
journal, June 2016

Burdakov, Oleg; Gong, Lujin; Zikrin, Spartak
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A dense initialization for limited-memory quasi-Newton methods
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Brust, Johannes; Burdakov, Oleg; Erway, Jennifer B.
Computational Optimization and Applications, Vol. 74, Issue 1
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Benchmarking optimization software with performance profiles
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Dolan, Elizabeth D.; Moré, Jorge J.
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Updating the Inverse of a Matrix
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On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
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preprint, January 2017

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Benchmarking Optimization Software with Performance Profiles
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Title: Large-Scale Quasi-Newton Trust-Region Methods With Low-Dimensional Linear Equality Constraints

Abstract

Citation Formats

Computing a Trust Region Step journal, September 1983

Representations of quasi-Newton matrices and their use in limited memory methods journal, January 1994

A trust region method based on interior point techniques for nonlinear programming journal, November 2000

A trust region algorithm for equality constrained optimization journal, November 1990

Compact representation of the full Broyden class of quasi-Newton updates: Compact Representation of the Full Broyden Class of Quasi-Newton Updates journal, May 2018

On the Implementation of an Algorithm for Large-Scale Equality Constrained Optimization journal, August 1998

On efficiently combining limited-memory and trust-region techniques journal, June 2016

A Trust Region Algorithm for Equality Constrained Minimization: Convergence Properties and Implementation journal, June 1985

On solving L-SR1 trust-region subproblems journal, September 2016

The Conjugate Gradient Method and Trust Regions in Large Scale Optimization journal, June 1983

A dense initialization for limited-memory quasi-Newton methods journal, May 2019

Benchmarking optimization software with performance profiles journal, January 2002

Algorithm 943: MSS: MATLAB Software for L-BFGS Trust-Region Subproblems for Large-Scale Optimization journal, June 2014

Updating the Inverse of a Matrix journal, June 1989

On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming journal, April 2005

An Interior Point Algorithm for Large-Scale Nonlinear Programming journal, January 1999

Compact representation of the full Broyden class of quasi-Newton updates preprint, January 2017

Benchmarking Optimization Software with Performance Profiles text, January 2001

Computing a Trust Region Step
journal, September 1983

Representations of quasi-Newton matrices and their use in limited memory methods
journal, January 1994

A trust region method based on interior point techniques for nonlinear programming
journal, November 2000

A trust region algorithm for equality constrained optimization
journal, November 1990

Compact representation of the full Broyden class of quasi-Newton updates: Compact Representation of the Full Broyden Class of Quasi-Newton Updates
journal, May 2018

On the Implementation of an Algorithm for Large-Scale Equality Constrained Optimization
journal, August 1998

On efficiently combining limited-memory and trust-region techniques
journal, June 2016

A Trust Region Algorithm for Equality Constrained Minimization: Convergence Properties and Implementation
journal, June 1985

On solving L-SR1 trust-region subproblems
journal, September 2016

The Conjugate Gradient Method and Trust Regions in Large Scale Optimization
journal, June 1983

A dense initialization for limited-memory quasi-Newton methods
journal, May 2019

Benchmarking optimization software with performance profiles
journal, January 2002

Algorithm 943: MSS: MATLAB Software for L-BFGS Trust-Region Subproblems for Large-Scale Optimization
journal, June 2014

Updating the Inverse of a Matrix
journal, June 1989

On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
journal, April 2005

An Interior Point Algorithm for Large-Scale Nonlinear Programming
journal, January 1999

Compact representation of the full Broyden class of quasi-Newton updates
preprint, January 2017

Benchmarking Optimization Software with Performance Profiles
text, January 2001