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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:
ORCiD logo [1];  [2];  [3]
  1. Argonne National Lab. (ANL), Lemont, IL (United States)
  2. Univ. of California, Merced, CA (United States)
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1575872
Report Number(s):
LLNL-JRNL-755231
Journal ID: ISSN 0926-6003; 942036
Grant/Contract Number:  
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; Linear equality constraints; Quasi-Newton; L-BFGS; Trust-region algorithm; Compact representation; Eigendecomposition; 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.
Brust, Johannes J., Marcia, Roummel F., & Petra, Cosmin G. Large-scale quasi-Newton trust-region methods with low-dimensional linear equality constraints. United States. doi:10.1007/s10589-019-00127-4.
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. doi:10.1007/s10589-019-00127-4.
@article{osti_1575872,
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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