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On solving L-SR1 trust-region subproblems

Author

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  • Johannes Brust

    (University of California, Merced)

  • Jennifer B. Erway

    (Wake Forest University)

  • Roummel F. Marcia

    (University of California, Merced)

Abstract

In this article, we consider solvers for large-scale trust-region subproblems when the quadratic model is defined by a limited-memory symmetric rank-one (L-SR1) quasi-Newton matrix. We propose a solver that exploits the compact representation of L-SR1 matrices. Our approach makes use of both an orthonormal basis for the eigenspace of the L-SR1 matrix and the Sherman–Morrison–Woodbury formula to compute global solutions to trust-region subproblems. To compute the optimal Lagrange multiplier for the trust-region constraint, we use Newton’s method with a judicious initial guess that does not require safeguarding. A crucial property of this solver is that it is able to compute high-accuracy solutions even in the so-called hard case. Additionally, the optimal solution is determined directly by formula, not iteratively. Numerical experiments demonstrate the effectiveness of this solver.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:66:y:2017:i:2:d:10.1007_s10589-016-9868-3
    DOI: 10.1007/s10589-016-9868-3
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    References listed on IDEAS

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    1. Henry Wolkowicz, 1994. "Measures for Symmetric Rank-One Updates," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 815-830, November.
    2. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, June.
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    Cited by:

    1. 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.
    2. Nataša Krejić & Nataša Krklec Jerinkić & Ángeles Martínez & Mahsa Yousefi, 2024. "A non-monotone trust-region method with noisy oracles and additional sampling," Computational Optimization and Applications, Springer, vol. 89(1), pages 247-278, September.

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