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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. 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).
    2. 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.
    3. 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.
    4. Stephen M. Robinson, 1992. "Normal Maps Induced by Linear Transformations," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 691-714, August.
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