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Proximal Bundle Method for Nonsmooth and Nonconvex Multiobjective Optimization

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Mathematical Modeling and Optimization of Complex Structures

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 40))

Abstract

We present a proximal bundle method for finding weakly Pareto optimal solutions to constrained nonsmooth programming problems with multiple objectives. The method is a generalization of proximal bundle approach for single objective optimization. The multiple objective functions are treated individually without employing any scalarization. The method is globally convergent and capable of handling several nonconvex locally Lipschitz continuous objective functions subject to nonlinear (possibly nondifferentiable) constraints. Under some generalized convexity assumptions, we prove that the method finds globally weakly Pareto optimal solutions. Concluding, some numerical examples illustrate the properties and applicability of the method.

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Acknowledgments

This work is financially supported by the University of Turku and the Vilho, Yrjö and Kalle Väisälä foundation.

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Authors and Affiliations

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

    Marko M. Mäkelä, Napsu Karmitsa & Outi Wilppu

Authors
  1. Marko M. Mäkelä
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  2. Napsu Karmitsa
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  3. Outi Wilppu
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Corresponding author

Correspondence to Marko M. Mäkelä .

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Editors and Affiliations

  1. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Pekka Neittaanmäki

  2. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Sergey Repin

  3. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Tero Tuovinen

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Mäkelä, M.M., Karmitsa, N., Wilppu, O. (2016). Proximal Bundle Method for Nonsmooth and Nonconvex Multiobjective Optimization. In: Neittaanmäki, P., Repin, S., Tuovinen, T. (eds) Mathematical Modeling and Optimization of Complex Structures. Computational Methods in Applied Sciences, vol 40. Springer, Cham. https://doi.org/10.1007/978-3-319-23564-6_12

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  • DOI: https://doi.org/10.1007/978-3-319-23564-6_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23563-9

  • Online ISBN: 978-3-319-23564-6

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