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

Author

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  • Johannes J. Brust

    (Argonne National Laboratory)

  • Roummel F. Marcia

    (University of California Merced)

  • Cosmin G. Petra

    (Lawrence Livermore National Laboratory)

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.

Suggested Citation

  • Johannes J. Brust & Roummel F. Marcia & Cosmin G. Petra, 2019. "Large-scale quasi-Newton trust-region methods with low-dimensional linear equality constraints," Computational Optimization and Applications, Springer, vol. 74(3), pages 669-701, December.
    • Handle: RePEc:spr:coopap:v:74:y:2019:i:3:d:10.1007_s10589-019-00127-4
    DOI: 10.1007/s10589-019-00127-4
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    References listed on IDEAS

    as
    1. Johannes Brust & Oleg Burdakov & Jennifer B. Erway & Roummel F. Marcia, 2019. "A dense initialization for limited-memory quasi-Newton methods," Computational Optimization and Applications, Springer, vol. 74(1), pages 121-142, September.
    2. Oleg Burdakov & José Martínez & Elvio Pilotta, 2002. "A Limited-Memory Multipoint Symmetric Secant Method for Bound Constrained Optimization," Annals of Operations Research, Springer, vol. 117(1), pages 51-70, November.
    3. Johannes Brust & Jennifer B. Erway & Roummel F. Marcia, 2017. "On solving L-SR1 trust-region subproblems," Computational Optimization and Applications, Springer, vol. 66(2), pages 245-266, March.
    Full references (including those not matched with items on IDEAS)

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