Large-scale quasi-Newton trust-region methods with low-dimensional linear equality constraints

Johannes J. Brust (), Roummel F. Marcia () and Cosmin G. Petra ()
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Johannes J. Brust: Argonne National Laboratory
Roummel F. Marcia: University of California Merced
Cosmin G. Petra: Lawrence Livermore National Laboratory

Computational Optimization and Applications, 2019, vol. 74, issue 3, No 4, 669-701

Abstract: Abstract We propose two limited-memory BFGS (L-BFGS) trust-region methods for large-scale optimization with linear equality constraints. 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.

Keywords: Linear equality constraints; Quasi-Newton; L-BFGS; Trust-region algorithm; Compact representation; Eigendecomposition; Shape-changing norm (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10589-019-00127-4

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