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On Local Nonglobal Minimum of Trust-Region Subproblem and Extension

Author

Listed:
  • Jiulin Wang

    (Fudan University)

  • Mengmeng Song

    (Beihang University)

  • Yong Xia

    (Beihang University)

Abstract

The local nonglobal minimizer of the trust-region subproblem, if it exists, is shown to have the second smallest objective function value among all KKT points. This new property is extended to the p-regularized subproblem. As a corollary, we show for the first time that finding the local nonglobal minimizer of the Nesterov–Polyak subproblem corresponds to a generalized eigenvalue problem.

Suggested Citation

  • Jiulin Wang & Mengmeng Song & Yong Xia, 2022. "On Local Nonglobal Minimum of Trust-Region Subproblem and Extension," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 707-722, November.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:2:d:10.1007_s10957-022-02115-x
    DOI: 10.1007/s10957-022-02115-x
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    References listed on IDEAS

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    1. Maziar Salahi & Akram Taati & Henry Wolkowicz, 2017. "Local nonglobal minima for solving large-scale extended trust-region subproblems," Computational Optimization and Applications, Springer, vol. 66(2), pages 223-244, March.
    2. NESTEROV, Yurii & POLYAK, B.T., 2006. "Cubic regularization of Newton method and its global performance," LIDAM Reprints CORE 1927, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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