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A fast gradient and function sampling method for finite-max functions

Author

Listed:
  • Elias S. Helou

    (University of São Paulo)

  • Sandra A. Santos

    (University of Campinas)

  • Lucas E. A. Simões

    (University of Campinas)

Abstract

This paper proposes an algorithm for the unconstrained minimization of a class of nonsmooth and nonconvex functions that can be written as finite-max functions. A gradient and function-based sampling method is proposed which, under special circumstances, either moves superlinearly to a minimizer of the problem of interest or improves the optimality certificate. Global and local convergence analysis are presented, as well as examples that illustrate the obtained theoretical results.

Suggested Citation

  • Elias S. Helou & Sandra A. Santos & Lucas E. A. Simões, 2018. "A fast gradient and function sampling method for finite-max functions," Computational Optimization and Applications, Springer, vol. 71(3), pages 673-717, December.
    • Handle: RePEc:spr:coopap:v:71:y:2018:i:3:d:10.1007_s10589-018-0030-2
    DOI: 10.1007/s10589-018-0030-2
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    References listed on IDEAS

    as
    1. Milagros Loreto & Hugo Aponte & Debora Cores & Marcos Raydan, 2017. "Nonsmooth spectral gradient methods for unconstrained optimization," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(4), pages 529-553, December.
    2. Jianzhong Zhang & Nae-Heon Kim & L. Lasdon, 1985. "An Improved Successive Linear Programming Algorithm," Management Science, INFORMS, vol. 31(10), pages 1312-1331, October.
    3. Elias Salomão Helou & Sandra A. Santos & Lucas E. A. Simões, 2017. "On the Local Convergence Analysis of the Gradient Sampling Method for Finite Max-Functions," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 137-157, October.
    4. Peng, Chengbin & Jin, Xiaogang & Shi, Meixia, 2010. "Epidemic threshold and immunization on generalized networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 549-560.
    5. J. V. Burke & A. S. Lewis & M. L. Overton, 2002. "Approximating Subdifferentials by Random Sampling of Gradients," Mathematics of Operations Research, INFORMS, vol. 27(3), pages 567-584, August.
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    Cited by:

    1. Morteza Maleknia & Mostafa Shamsi, 2020. "A Gradient Sampling Method Based on Ideal Direction for Solving Nonsmooth Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 181-204, October.
    2. M. Maleknia & M. Shamsi, 2020. "A new method based on the proximal bundle idea and gradient sampling technique for minimizing nonsmooth convex functions," Computational Optimization and Applications, Springer, vol. 77(2), pages 379-409, November.

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