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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Turku, 20014, Turku, Finland

    Outi Montonen & Kaisa Joki

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  1. Outi Montonen
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  2. Kaisa Joki
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Correspondence to Outi Montonen.

Additional information

The research is financially supported by University of Turku Graduate School UTUGS Matti Programme, and Academy of Finland Project No. 294002. The authors gratefully thank Marko Mäkelä and Napsu Karmitsa for their valuable comments and encouragement during the preparation of this paper.

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Montonen, O., Joki, K. Bundle-based descent method for nonsmooth multiobjective DC optimization with inequality constraints. J Glob Optim 72, 403–429 (2018). https://doi.org/10.1007/s10898-018-0651-0

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