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

Journal Article · · Computational Optimization and Applications
ORCiD logo [1];  [2];  [3]
  1. Argonne National Lab. (ANL), Argonne, IL (United States)
  2. Univ. of California, Merced, CA (United States)
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
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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.

Research Organization:
Argonne National Laboratory (ANL), Argonne, IL (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC02-06CH11357; AC52-07NA27344
OSTI ID:
1596681
Alternate ID(s):
OSTI ID: 1575872
Report Number(s):
LLNL-JRNL-755231; 154974
Journal Information:
Computational Optimization and Applications, Vol. 74, Issue 3; ISSN 0926-6003
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 5 works
Citation information provided by
Web of Science

References (18)

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A dense initialization for limited-memory quasi-Newton methods journal May 2019
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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
Representations of quasi-Newton matrices and their use in limited memory methods journal January 1994

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Related Subjects

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