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Numerical infinitesimals in a variable metric method for convex nonsmooth optimization

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  • Gaudioso, Manlio
  • Giallombardo, Giovanni
  • Mukhametzhanov, Marat

Abstract

The objective of the paper is to evaluate the impact of the infinity computing paradigm on practical solution of nonsmooth unconstrained optimization problems, where the objective function is assumed to be convex and not necessarily differentiable. For such family of problems, the occurrence of discontinuities in the derivatives may result in failures of the algorithms suited for smooth problems.

Suggested Citation

  • Gaudioso, Manlio & Giallombardo, Giovanni & Mukhametzhanov, Marat, 2018. "Numerical infinitesimals in a variable metric method for convex nonsmooth optimization," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 312-320.
    • Handle: RePEc:eee:apmaco:v:318:y:2018:i:c:p:312-320
    DOI: 10.1016/j.amc.2017.07.057
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    References listed on IDEAS

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    1. Lolli, Gabriele, 2015. "Metamathematical investigations on the theory of Grossone," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 3-14.
    2. Demyanov, Alexey V. & Fuduli, Antonio & Miglionico, Giovanna, 2007. "A bundle modification strategy for convex minimization," European Journal of Operational Research, Elsevier, vol. 180(1), pages 38-47, July.
    3. Adil Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2014. "Introduction to Nonsmooth Optimization," Springer Books, Springer, edition 127, number 978-3-319-08114-4, November.
    4. A. Fuduli & M. Gaudioso, 2006. "Tuning Strategy for the Proximity Parameter in Convex Minimization," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 95-112, July.
    5. A. M. Bagirov & B. Karasözen & M. Sezer, 2008. "Discrete Gradient Method: Derivative-Free Method for Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 317-334, May.
    6. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Napsu Karmitsa, 2015. "Diagonal Bundle Method for Nonsmooth Sparse Optimization," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 889-905, September.
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    Citations

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    Cited by:

    1. Fiaschi, Lorenzo & Cococcioni, Marco, 2021. "Non-Archimedean game theory: A numerical approach," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    2. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2022. "Essentials of numerical nonsmooth optimization," Annals of Operations Research, Springer, vol. 314(1), pages 213-253, July.
    3. Renato Leone & Giovanni Fasano & Massimo Roma & Yaroslav D. Sergeyev, 2020. "Iterative Grossone-Based Computation of Negative Curvature Directions in Large-Scale Optimization," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 554-589, August.
    4. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2020. "Essentials of numerical nonsmooth optimization," 4OR, Springer, vol. 18(1), pages 1-47, March.
    5. Falcone, Alberto & Garro, Alfredo & Mukhametzhanov, Marat S. & Sergeyev, Yaroslav D., 2021. "A Simulink-based software solution using the Infinity Computer methodology for higher order differentiation," Applied Mathematics and Computation, Elsevier, vol. 409(C).

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