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Bundle-based descent method for nonsmooth multiobjective DC optimization with inequality constraints

Author

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  • Outi Montonen

    (University of Turku)

  • Kaisa Joki

    (University of Turku)

Abstract

Multiobjective DC optimization problems arise naturally, for example, in data classification and cluster analysis playing a crucial role in data mining. In this paper, we propose a new multiobjective double bundle method designed for nonsmooth multiobjective optimization problems having objective and constraint functions which can be presented as a difference of two convex (DC) functions. The method is of the descent type and it generalizes the ideas of the double bundle method for multiobjective and constrained problems. We utilize the special cutting plane model angled for the DC improvement function such that the convex and the concave behaviour of the function is captured. The method is proved to be finitely convergent to a weakly Pareto stationary point under mild assumptions. Finally, we consider some numerical experiments and compare the solutions produced by our method with the method designed for general nonconvex multiobjective problems. This is done in order to validate the usage of the method aimed specially for DC objectives instead of a general nonconvex method.

Suggested Citation

  • Outi Montonen & Kaisa Joki, 2018. "Bundle-based descent method for nonsmooth multiobjective DC optimization with inequality constraints," Journal of Global Optimization, Springer, vol. 72(3), pages 403-429, November.
    • Handle: RePEc:spr:jglopt:v:72:y:2018:i:3:d:10.1007_s10898-018-0651-0
    DOI: 10.1007/s10898-018-0651-0
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    References listed on IDEAS

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    1. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
    2. Qu, Shaojian & Liu, Chen & Goh, Mark & Li, Yijun & Ji, Ying, 2014. "Nonsmooth multiobjective programming with quasi-Newton methods," European Journal of Operational Research, Elsevier, vol. 235(3), pages 503-510.
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    4. Kaisa Joki & Adil M. Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2017. "A proximal bundle method for nonsmooth DC optimization utilizing nonconvex cutting planes," Journal of Global Optimization, Springer, vol. 68(3), pages 501-535, July.
    5. Shaojian Qu & Mark Goh & Soon-Yi Wu & Robert Souza, 2014. "Multiobjective DC programs with infinite convex constraints," Journal of Global Optimization, Springer, vol. 59(1), pages 41-58, May.
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    7. 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:

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