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A class of exact penalty functions and penalty algorithms for nonsmooth constrained optimization problems

Author

Listed:
  • Qian Liu

    (Shandong Normal University)

  • Yuqing Xu

    (Shandong Normal University)

  • Yang Zhou

    (Shandong Normal University)

Abstract

In this paper, a class of smoothing penalty functions is proposed for optimization problems with equality, inequality and bound constraints. It is proved exact, under the condition of weakly generalized Mangasarian–Fromovitz constraint qualification, in the sense that each local optimizer of the penalty function corresponds to a local optimizer of the original problem. Furthermore, necessary and sufficient conditions are discussed for the inverse proposition of exact penalization. Based on the theoretical results in this paper, a class of smoothing penalty algorithms with feasibility verification is presented. Theories on the penalty exactness, feasibility verification and global convergence of the proposed algorithm are presented. Numerical results show that this algorithm is effective for nonsmooth nonconvex constrained optimization problems.

Suggested Citation

  • Qian Liu & Yuqing Xu & Yang Zhou, 2020. "A class of exact penalty functions and penalty algorithms for nonsmooth constrained optimization problems," Journal of Global Optimization, Springer, vol. 76(4), pages 745-768, April.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:4:d:10.1007_s10898-019-00842-6
    DOI: 10.1007/s10898-019-00842-6
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    References listed on IDEAS

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    1. Changyu Wang & Cheng Ma & Jinchuan Zhou, 2014. "A new class of exact penalty functions and penalty algorithms," Journal of Global Optimization, Springer, vol. 58(1), pages 51-73, January.
    2. Mengwei Xu & Jane Ye & Liwei Zhang, 2015. "Smoothing augmented Lagrangian method for nonsmooth constrained optimization problems," Journal of Global Optimization, Springer, vol. 62(4), pages 675-694, August.
    3. Changyu Wang & Qian Liu & Biao Qu, 2017. "Global saddle points of nonlinear augmented Lagrangian functions," Journal of Global Optimization, Springer, vol. 68(1), pages 125-146, May.
    4. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    2. Suxia Ma & Yuelin Gao & Bo Zhang & Wenlu Zuo, 2022. "A New Nonparametric Filled Function Method for Integer Programming Problems with Constraints," Mathematics, MDPI, vol. 10(5), pages 1-16, February.

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