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Efficient proximal subproblem solvers for a nonsmooth trust-region method

Author

Listed:
  • Robert J. Baraldi

    (Sandia National Laboratories)

  • Drew P. Kouri

    (Sandia National Laboratories)

Abstract

In [R. J. Baraldi and D. P. Kouri, Mathematical Programming, (2022), pp. 1-40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex and nonsmooth convex function. The principle expense of this method is in computing a trial iterate that satisfies the so-called fraction of Cauchy decrease condition—a bound that ensures the trial iterate produces sufficient decrease of the subproblem model. In this paper, we expound on various proximal trust-region subproblem solvers that generalize traditional trust-region methods for smooth unconstrained and convex-constrained problems. We introduce a simplified spectral proximal gradient solver, a truncated nonlinear conjugate gradient solver, and a dogleg method. We compare algorithm performance on examples from data science and PDE-constrained optimization.

Suggested Citation

  • Robert J. Baraldi & Drew P. Kouri, 2025. "Efficient proximal subproblem solvers for a nonsmooth trust-region method," Computational Optimization and Applications, Springer, vol. 90(1), pages 193-226, January.
    • Handle: RePEc:spr:coopap:v:90:y:2025:i:1:d:10.1007_s10589-024-00628-x
    DOI: 10.1007/s10589-024-00628-x
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    References listed on IDEAS

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    1. Stefania Bellavia & Gianmarco Gurioli & Benedetta Morini & Philippe Louis Toint, 2023. "The Impact of Noise on Evaluation Complexity: The Deterministic Trust-Region Case," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 700-729, February.
    2. Birgin, Ernesto G. & Martínez, Jose Mario & Raydan, Marcos, 2014. "Spectral Projected Gradient Methods: Review and Perspectives," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i03).
    3. Stephen M. Robinson, 1992. "Normal Maps Induced by Linear Transformations," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 691-714, August.
    4. María Maciel & María Mendonça & Adriana Verdiell, 2013. "Monotone and nonmonotone trust-region-based algorithms for large scale unconstrained optimization problems," Computational Optimization and Applications, Springer, vol. 54(1), pages 27-43, January.
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