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Constrained Nonconvex Nonsmooth Optimization via Proximal Bundle Method

Author

Listed:
  • Yang Yang

    (Dalian University of Technology)

  • Liping Pang

    (Dalian University of Technology)

  • Xuefei Ma

    (Syracuse University)

  • Jie Shen

    (Liaoning Normal University)

Abstract

In this paper, we consider a constrained nonconvex nonsmooth optimization, in which both objective and constraint functions may not be convex or smooth. With the help of the penalty function, we transform the problem into an unconstrained one and design an algorithm in proximal bundle method in which local convexification of the penalty function is utilized to deal with it. We show that, if adding a special constraint qualification, the penalty function can be an exact one, and the sequence generated by our algorithm converges to the KKT points of the problem under a moderate assumption. Finally, some illustrative examples are given to show the good performance of our algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:163:y:2014:i:3:d:10.1007_s10957-014-0523-9
    DOI: 10.1007/s10957-014-0523-9
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    References listed on IDEAS

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    1. Krzysztof Czesław Kiwiel, 1985. "A Linearization Algorithm for Nonsmooth Minimization," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 185-194, May.
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    Cited by:

    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. Najmeh Hoseini Monjezi & S. Nobakhtian, 2019. "A new infeasible proximal bundle algorithm for nonsmooth nonconvex constrained optimization," Computational Optimization and Applications, Springer, vol. 74(2), pages 443-480, November.
    3. Najmeh Hoseini Monjezi & S. Nobakhtian, 2021. "A filter proximal bundle method for nonsmooth nonconvex constrained optimization," Journal of Global Optimization, Springer, vol. 79(1), pages 1-37, January.
    4. Jian Lv & Li-Ping Pang & Fan-Yun Meng, 2018. "A proximal bundle method for constrained nonsmooth nonconvex optimization with inexact information," Journal of Global Optimization, Springer, vol. 70(3), pages 517-549, March.
    5. Pang, Li-Ping & Chen, Shuang & Wang, Jin-He, 2015. "Risk management in portfolio applications of non-convex stochastic programming," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 565-575.
    6. 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.
    7. Xiaoliang Wang & Liping Pang & Qi Wu & Mingkun Zhang, 2021. "An Adaptive Proximal Bundle Method with Inexact Oracles for a Class of Nonconvex and Nonsmooth Composite Optimization," Mathematics, MDPI, vol. 9(8), pages 1-27, April.

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