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

Authors:

Jennifer B. Erway,

Roummel F. MarciaAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 40, Issue 4

Article No.: 28, Pages 1 - 12

https://doi.org/10.1145/2616588

Published: 08 July 2014 Publication History

Abstract

A MATLAB implementation of the Moré-Sorensen sequential (MSS) method is presented. The MSS method computes the minimizer of a quadratic function defined by a limited-memory BFGS matrix subject to a two-norm trust-region constraint. This solver is an adaptation of the Moré-Sorensen direct method into an L-BFGS setting for large-scale optimization. The MSS method makes use of a recently proposed stable fast direct method for solving large shifted BFGS systems of equations [Erway and Marcia 2012; Erway et al. 2012] and is able to compute solutions to any user-defined accuracy. This MATLAB implementation is a matrix-free iterative method for large-scale optimization. Numerical experiments on the CUTEr [Bongartz et al. 1995; Gould et al. 2003]) suggest that using the MSS method as a trust-region subproblem solver can require significantly fewer function and gradient evaluations needed by a trust-region method as compared with the Steihaug-Toint method.

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References

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Cited By

Brust JErway JMarcia R(2024)Shape-changing trust-region methods using multipoint symmetric secant matricesOptimization Methods and Software10.1080/10556788.2023.2296441(1-18)Online publication date: 24-Jan-2024
https://doi.org/10.1080/10556788.2023.2296441
Quintana-Ortí GHernando FIgual F(2023)Algorithm 1033: Parallel Implementations for Computing the Minimum Distance of a Random Linear Code on Distributed-memory ArchitecturesACM Transactions on Mathematical Software10.1145/357338349:1(1-24)Online publication date: 21-Mar-2023
https://dl.acm.org/doi/10.1145/3573383
Demeure NChevalier CDenis CDossantos-Uzarralde P(2023)Algorithm 1029: Encapsulated Error, a Direct Approach to Evaluate Floating-Point AccuracyACM Transactions on Mathematical Software10.1145/354920548:4(1-16)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1145/3549205
Show More Cited By

Index Terms

Algorithm 943: MSS: MATLAB Software for L-BFGS Trust-Region Subproblems for Large-Scale Optimization
1. Mathematics of computing
  1. Mathematical software

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 40, Issue 4

June 2014

154 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/2639949

Editor:
Michael A. Heroux
Sandia National Laboratories

Issue’s Table of Contents

Copyright © 2014 ACM.

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Association for Computing Machinery

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Publication History

Published: 08 July 2014

Accepted: 01 November 2013

Revised: 01 July 2013

Received: 01 December 2012

Published in TOMS Volume 40, Issue 4

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Cited By

Brust JErway JMarcia R(2024)Shape-changing trust-region methods using multipoint symmetric secant matricesOptimization Methods and Software10.1080/10556788.2023.2296441(1-18)Online publication date: 24-Jan-2024
https://doi.org/10.1080/10556788.2023.2296441
Quintana-Ortí GHernando FIgual F(2023)Algorithm 1033: Parallel Implementations for Computing the Minimum Distance of a Random Linear Code on Distributed-memory ArchitecturesACM Transactions on Mathematical Software10.1145/357338349:1(1-24)Online publication date: 21-Mar-2023
https://dl.acm.org/doi/10.1145/3573383
Demeure NChevalier CDenis CDossantos-Uzarralde P(2023)Algorithm 1029: Encapsulated Error, a Direct Approach to Evaluate Floating-Point AccuracyACM Transactions on Mathematical Software10.1145/354920548:4(1-16)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1145/3549205
Erway JRezapour M(2023)A new multipoint symmetric secant method with a dense initial matrixOptimization Methods and Software10.1080/10556788.2023.216799338:4(698-722)Online publication date: 6-Feb-2023
https://doi.org/10.1080/10556788.2023.2167993
Brust JBurdakov OErway JMarcia R(2022)Algorithm 1030: SC-SR1: MATLAB Software for Limited-memory SR1 Trust-region MethodsACM Transactions on Mathematical Software10.1145/355026948:4(1-33)Online publication date: 19-Dec-2022
https://dl.acm.org/doi/10.1145/3550269
Brust JMarcia RPetra C(2019)Large-scale quasi-Newton trust-region methods with low-dimensional linear equality constraintsComputational Optimization and Applications10.1007/s10589-019-00127-4Online publication date: 5-Sep-2019
https://doi.org/10.1007/s10589-019-00127-4
Brust JErway JMarcia R(2017)On solving L-SR1 trust-region subproblemsComputational Optimization and Applications10.1007/s10589-016-9868-366:2(245-266)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1007/s10589-016-9868-3
Burdakov OGong LZikrin SYuan Y(2016)On efficiently combining limited-memory and trust-region techniquesMathematical Programming Computation10.1007/s12532-016-0109-79:1(101-134)Online publication date: 27-Jun-2016
https://doi.org/10.1007/s12532-016-0109-7
Bates JShiozaki T(2015)Fully relativistic complete active space self-consistent field for large molecules: Quasi-second-order minimax optimizationThe Journal of Chemical Physics10.1063/1.4906344142:4Online publication date: 27-Jan-2015
https://doi.org/10.1063/1.4906344

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