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Bundle Methods for Nonsmooth DC Optimization

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Numerical Nonsmooth Optimization

Abstract

This chapter is devoted to algorithms for solving nonsmooth unconstrained difference of convex optimization problems. Different types of stationarity conditions are discussed and the relationship between sets of different stationary points (critical, Clarke stationary and inf-stationary) is established. Bundle methods are developed based on a nonconvex piecewise linear model of the objective function and the convergence of these methods is studied. Numerical results are presented to demonstrate the performance of the methods.

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Acknowledgements

This work was financially supported by the University of Turku, the Academy of Finland (Projects 294002 and 319274) and the Australian Government through the Australian Research Council’s Discovery funding scheme (Project No. DP190100580).

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Turku, Turku, Finland

    Kaisa Joki

  2. School of Science, Engineering and Information Technology, Federation University Australia, Ballarat, VIC, Australia

    Adil M. Bagirov

Authors
  1. Kaisa Joki
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  2. Adil M. Bagirov
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Corresponding author

Correspondence to Kaisa Joki .

Editor information

Editors and Affiliations

  1. School of Science, Engineering and Information Technology, Federation University Australia, Ballarat, VIC, Australia

    Adil M. Bagirov

  2. Department of Informatics, Modeling, Electronics and System Engineering, University of Calabria, Rende (CS), Italy

    Manlio Gaudioso

  3. Department of Mathematics and Statistics, University of Turku, Turku, Finland

    Napsu Karmitsa

  4. Department of Mathematics and Statistics, University of Turku, Turku, Finland

    Marko M. Mäkelä

  5. School of Science, Engineering and Information Technology, Federation University Australia, Ballarat, VIC, Australia

    Sona Taheri

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Joki, K., Bagirov, A.M. (2020). Bundle Methods for Nonsmooth DC Optimization. In: Bagirov, A., Gaudioso, M., Karmitsa, N., Mäkelä, M., Taheri, S. (eds) Numerical Nonsmooth Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-34910-3_8

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