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Adaptive Sampling Stochastic Multigradient Algorithm for Stochastic Multiobjective Optimization

Author

Listed:
  • Yong Zhao

    (Chongqing Jiaotong University
    Chongqing University)

  • Wang Chen

    (Chongqing Normal University)

  • Xinmin Yang

    (Chongqing Normal University
    Chongqing Normal University)

Abstract

In this paper, we propose an adaptive sampling stochastic multigradient algorithm for solving stochastic multiobjective optimization problems. Instead of requiring additional storage or computation of full gradients, the proposed method reduces variance by adaptively controlling the sample size used. Without the convexity assumption on the objective functions, we obtain that the proposed algorithm converges to Pareto stationary points in almost surely. We then analyze the convergence rates of the proposed algorithm. Numerical experiments are presented to demonstrate the effectiveness of the proposed algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:200:y:2024:i:1:d:10.1007_s10957-023-02334-w
    DOI: 10.1007/s10957-023-02334-w
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    References listed on IDEAS

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    1. Fliege, Jörg & Werner, Ralf, 2014. "Robust multiobjective optimization & applications in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 422-433.
    2. 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.
    3. 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.
    4. Gabriele Eichfelder & Leo Warnow, 2022. "An approximation algorithm for multi-objective optimization problems using a box-coverage," Journal of Global Optimization, Springer, vol. 83(2), pages 329-357, June.
    5. Matthias Ehrgott, 2005. "Multicriteria Optimization," Springer Books, Springer, edition 0, number 978-3-540-27659-3, December.
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