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

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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.

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Acknowledgements

We would like to thank the referees for their valuable and helpful comments on our manuscript.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong, China

    Qian Liu, Yuqing Xu & Yang Zhou

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  1. Qian Liu
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  2. Yuqing Xu
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  3. Yang Zhou
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Correspondence to Yang Zhou.

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The work in this paper was supported by the National Natural Science Foundation of China (Nos. 11626147, 11271226) and Shandong Provincial Natural Science Foundation, China (No. ZR2019PA004).

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Liu, Q., Xu, Y. & Zhou, Y. A class of exact penalty functions and penalty algorithms for nonsmooth constrained optimization problems. J Glob Optim 76, 745–768 (2020). https://doi.org/10.1007/s10898-019-00842-6

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  • DOI: https://doi.org/10.1007/s10898-019-00842-6

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