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Diagonal Bundle Method for Nonsmooth Sparse Optimization

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  • Napsu Karmitsa

    (University of Turku)

Abstract

We propose an efficient diagonal bundle method for sparse nonsmooth, possibly nonconvex optimization. The convergence of the proposed method is proved for locally Lipschitz continuous functions, which are not necessary differentiable or convex. The numerical experiments have been made using problems with up to million variables. The results to be presented confirm the usability of the diagonal bundle method especially for extremely large-scale problems.

Suggested Citation

  • Napsu Karmitsa, 2015. "Diagonal Bundle Method for Nonsmooth Sparse Optimization," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 889-905, September.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:3:d:10.1007_s10957-014-0666-8
    DOI: 10.1007/s10957-014-0666-8
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    References listed on IDEAS

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    1. Napsu Karmitsa & Mario Tanaka Filho & José Herskovits, 2011. "Globally Convergent Cutting Plane Method for Nonconvex Nonsmooth Minimization," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 528-549, March.
    2. P. S. Bradley & Usama M. Fayyad & O. L. Mangasarian, 1999. "Mathematical Programming for Data Mining: Formulations and Challenges," INFORMS Journal on Computing, INFORMS, vol. 11(3), pages 217-238, August.
    3. E. Polak & J. O. Royset, 2003. "Algorithms for Finite and Semi-Infinite Min–Max–Min Problems Using Adaptive Smoothing Techniques," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 421-457, December.
    4. Adil Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2014. "Introduction to Nonsmooth Optimization," Springer Books, Springer, edition 127, number 978-3-319-08114-4, December.
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    Cited by:

    1. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2020. "Essentials of numerical nonsmooth optimization," 4OR, Springer, vol. 18(1), pages 1-47, March.
    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. 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.
    4. Karmitsa, Napsu & Bagirov, Adil M. & Taheri, Sona, 2017. "New diagonal bundle method for clustering problems in large data sets," European Journal of Operational Research, Elsevier, vol. 263(2), pages 367-379.

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