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Descent algorithm for nonsmooth stochastic multiobjective optimization

Author

Listed:
  • Fabrice Poirion

    (ONERA The French Aerospace Lab)

  • Quentin Mercier

    (ONERA The French Aerospace Lab)

  • Jean-Antoine Désidéri

    (INRIA)

Abstract

An algorithm for solving the expectation formulation of stochastic nonsmooth multiobjective optimization problems is proposed. The proposed method is an extension of the classical stochastic gradient algorithm to multiobjective optimization using the properties of a common descent vector defined in the deterministic context. The mean square and the almost sure convergence of the algorithm are proven. The algorithm efficiency is illustrated and assessed on an academic example.

Suggested Citation

  • Fabrice Poirion & Quentin Mercier & Jean-Antoine Désidéri, 2017. "Descent algorithm for nonsmooth stochastic multiobjective optimization," Computational Optimization and Applications, Springer, vol. 68(2), pages 317-331, November.
    • Handle: RePEc:spr:coopap:v:68:y:2017:i:2:d:10.1007_s10589-017-9921-x
    DOI: 10.1007/s10589-017-9921-x
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    References listed on IDEAS

    as
    1. Jörg Fliege & Huifu Xu, 2011. "Stochastic Multiobjective Optimization: Sample Average Approximation and Applications," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 135-162, October.
    2. J. V. Burke & A. S. Lewis & M. L. Overton, 2002. "Approximating Subdifferentials by Random Sampling of Gradients," Mathematics of Operations Research, INFORMS, vol. 27(3), pages 567-584, August.
    3. J. Cruz Neto & G. Silva & O. Ferreira & J. Lopes, 2013. "A subgradient method for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 461-472, April.
    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.
    5. Henri Bonnel & Julien Collonge, 2014. "Stochastic Optimization over a Pareto Set Associated with a Stochastic Multi-Objective Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 405-427, August.
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    Cited by:

    1. Yong Zhao & Wang Chen & Xinmin Yang, 2024. "Adaptive Sampling Stochastic Multigradient Algorithm for Stochastic Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 215-241, January.

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