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A class of infeasible proximal bundle methods for nonsmooth nonconvex multi-objective optimization problems

Author

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  • Li-Ping Pang

    (Dalian University of Technology
    Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province)

  • Fan-Yun Meng

    (Qingdao University of Technology)

  • Jian-Song Yang

    (Dalian University of Technology)

Abstract

We propose a class of infeasible proximal bundle methods for solving nonsmooth nonconvex multi-objective optimization problems. The proposed algorithms have no requirements on the feasibility of the initial points. In the algorithms, the multi-objective functions are handled directly without any scalarization procedure. To speed up the convergence of the infeasible algorithm, an acceleration technique, i.e., the penalty skill, is applied into the algorithm. The strategies are introduced to adjust the proximal parameters and penalty parameters. Under some wild assumptions, the sequence generated by infeasible proximal bundle methods converges to the globally Pareto solution of multi-objective optimization problems. Numerical results shows the good performance of the proposed algorithms.

Suggested Citation

  • Li-Ping Pang & Fan-Yun Meng & Jian-Song Yang, 2023. "A class of infeasible proximal bundle methods for nonsmooth nonconvex multi-objective optimization problems," Journal of Global Optimization, Springer, vol. 85(4), pages 891-915, April.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:4:d:10.1007_s10898-022-01242-z
    DOI: 10.1007/s10898-022-01242-z
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    References listed on IDEAS

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    1. Fan-Yun Meng & Li-Ping Pang & Jian Lv & Jin-He Wang, 2017. "An approximate bundle method for solving nonsmooth equilibrium problems," Journal of Global Optimization, Springer, vol. 68(3), pages 537-562, July.
    2. Yang Yang & Liping Pang & Xuefei Ma & Jie Shen, 2014. "Constrained Nonconvex Nonsmooth Optimization via Proximal Bundle Method," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 900-925, December.
    3. W. Hare & C. Sagastizábal & M. Solodov, 2016. "A proximal bundle method for nonsmooth nonconvex functions with inexact information," Computational Optimization and Applications, Springer, vol. 63(1), pages 1-28, January.
    4. Li-Ping Pang & Jian Lv & Jin-He Wang, 2016. "Constrained incremental bundle method with partial inexact oracle for nonsmooth convex semi-infinite programming problems," Computational Optimization and Applications, Springer, vol. 64(2), pages 433-465, June.
    5. 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.
    6. Vieira, D.A.G. & Lisboa, A.C., 2019. "A cutting-plane method to nonsmooth multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 275(3), pages 822-829.
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