Iterative Methods for Equality-Constrained Least Squares Problems

We consider the linear equality-constrained least squares problem (LSE) of minimizing ${\|c - Gx\|}_2 $, subject to the constraint $Ex = p$. A preconditioned conjugate gradient method is applied to the Kuhn-Tucker equations associated with the LSE problem. We show that our method is well suited for...

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Bibliographic Details
Published inSIAM journal on scientific and statistical computing Vol. 9; no. 5; pp. 892 - 906
Main Authors Barlow, J. L., Nichols, N. K., Plemmons, R. J.
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.09.1988
Subjects
Algorithms
Applied mathematics
Applied sciences
Computer science
Exact sciences and technology
Iterative methods
Methods
Operational research and scientific management
Operational research. Management science
Optimization
Optimization. Search problems
Conjugate gradient method
Least squares method
Optimization
Equality constraint
Constrained optimization
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ISSN0196-5204
1064-8275
2168-3417
1095-7197
DOI10.1137/0909061

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Summary:We consider the linear equality-constrained least squares problem (LSE) of minimizing ${\|c - Gx\|}_2 $, subject to the constraint $Ex = p$. A preconditioned conjugate gradient method is applied to the Kuhn-Tucker equations associated with the LSE problem. We show that our method is well suited for structural optimization problems in reliability analysis and optimal design. Numerical tests are performed on an Alliant FX/8 multiprocessor and a Cray-X-MP using some practical structural analysis data.
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ISSN:0196-5204
1064-8275
2168-3417
1095-7197
DOI:10.1137/0909061