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Local nonglobal minima for solving large-scale extended trust-region subproblems

Author

Listed:
  • Maziar Salahi

    (University of Guilan)

  • Akram Taati

    (University of Guilan)

  • Henry Wolkowicz

    (University of Waterloo)

Abstract

We study large-scale extended trust-region subproblems (eTRS) i.e., the minimization of a general quadratic function subject to a norm constraint, known as the trust-region subproblem (TRS) but with an additional linear inequality constraint. It is well known that strong duality holds for the TRS and that there are efficient algorithms for solving large-scale TRS problems. It is also known that there can exist at most one local non-global minimizer (LNGM) for TRS. We combine this with known characterizations for strong duality for eTRS and, in particular, connect this with the so-called hard case for TRS. We begin with a recent characterization of the minimum for the TRS via a generalized eigenvalue problem and extend this result to the LNGM. We then use this to derive an efficient algorithm that finds the global minimum for eTRS by solving at most three generalized eigenvalue problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:66:y:2017:i:2:d:10.1007_s10589-016-9867-4
    DOI: 10.1007/s10589-016-9867-4
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    Cited by:

    1. Temadher A. Almaadeed & Saeid Ansary Karbasy & Maziar Salahi & Abdelouahed Hamdi, 2022. "On Indefinite Quadratic Optimization over the Intersection of Balls and Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 246-264, July.
    2. 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.

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