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A note on the convergence of deterministic gradient sampling in nonsmooth optimization

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  • Bennet Gebken

    (Paderborn University)

Abstract

Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions.

Suggested Citation

  • Bennet Gebken, 2024. "A note on the convergence of deterministic gradient sampling in nonsmooth optimization," Computational Optimization and Applications, Springer, vol. 88(1), pages 151-165, May.
    • Handle: RePEc:spr:coopap:v:88:y:2024:i:1:d:10.1007_s10589-024-00552-0
    DOI: 10.1007/s10589-024-00552-0
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    References listed on IDEAS

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    1. Defeng Sun & Jie Sun, 2008. "Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 421-445, May.
    2. Robert Mifflin, 1977. "An Algorithm for Constrained Optimization with Semismooth Functions," Mathematics of Operations Research, INFORMS, vol. 2(2), pages 191-207, May.
    3. Bennet Gebken & Sebastian Peitz, 2021. "An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 696-723, March.
    4. Nezam Mahdavi-Amiri & Rohollah Yousefpour, 2012. "An Effective Nonsmooth Optimization Algorithm for Locally Lipschitz Functions," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 180-195, October.
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    Cited by:

    1. Bennet Gebken, 2025. "Analyzing the Speed of Convergence in Nonsmooth Optimization via the Goldstein subdifferential," Journal of Optimization Theory and Applications, Springer, vol. 206(3), pages 1-38, September.

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