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Global convergence of a class new smooth penalty algorithm for constrained optimization problem

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Abstract

In this paper, a class of smooth penalty functions is proposed for constrained optimization problem. It is put forward based on \(L_p\), a smooth function of a class of exact penalty function \({\ell _p}~\left( {p \in (0,1]} \right) \). Based on the class of penalty functions, a penalty algorithm is presented. Under the very weak condition, a perturbation theorem is set up. The global convergence of the algorithm is derived. This result generalizes some existing conclusions. Finally, numerical experiments on two examples demonstrate the effectiveness and efficiency of our algorithm.

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Acknowledgements

The authors would like to express their sincere thanks to the editor and the anonymous reviewers for their helpful comments and suggestions to improve this paper.

Funding

This research was supported by Natural Science Foundation of Shandong Province (ZR2021MA066).

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  1. Ruyu Wang and Daojin Song have contributed equally to this work.

Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255049, People’s Republic of China

    Wenling Zhao, Ruyu Wang & Daojin Song

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  1. Wenling Zhao
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  2. Ruyu Wang
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  3. Daojin Song
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Correspondence to Wenling Zhao.

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Zhao, W., Wang, R. & Song, D. Global convergence of a class new smooth penalty algorithm for constrained optimization problem. J. Appl. Math. Comput. 69, 3987–3997 (2023). https://doi.org/10.1007/s12190-023-01911-6

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  • DOI: https://doi.org/10.1007/s12190-023-01911-6

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