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A proximal bundle method for constrained nonsmooth nonconvex optimization with inexact information

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Abstract

We propose an inexact proximal bundle method for constrained nonsmooth nonconvex optimization problems whose objective and constraint functions are known through oracles which provide inexact information. The errors in function and subgradient evaluations might be unknown, but are merely bounded. To handle the nonconvexity, we first use the redistributed idea, and consider even more difficulties by introducing inexactness in the available information. We further examine the modified improvement function for a series of difficulties caused by the constrained functions. The numerical results show the good performance of our inexact method for a large class of nonconvex optimization problems. The approach is also assessed on semi-infinite programming problems, and some encouraging numerical experiences are provided.

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Acknowledgements

The authors wish to thank Editor-in-Chief Sergiy Butenko, the preceding managing editors and the anonymous reviewers for their helpful comments on the earlier version of this paper, which considerably improved both the presentation and the numerical experiments. We also gratefully acknowledge the support of the Huzhou science and technology plan on No. 2016GY03 and Natural Science Foundation of China Grant 11626051.

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Authors and Affiliations

  1. School of Finance, Zhejiang University of Finance and Economics, Hangzhou, 310018, China

    Jian Lv

  2. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Li-Ping Pang

  3. School of Computer, Qingdao Technological University, Qingdao, 266033, China

    Fan-Yun Meng

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  1. Jian Lv
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  2. Li-Ping Pang
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  3. Fan-Yun Meng
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Correspondence to Li-Ping Pang.

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Partially supported by Huzhou science and technology plan on No. 2016GY03 and Natural Science Foundation of China Grant 11626051.

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Lv, J., Pang, LP. & Meng, FY. A proximal bundle method for constrained nonsmooth nonconvex optimization with inexact information. J Glob Optim 70, 517–549 (2018). https://doi.org/10.1007/s10898-017-0565-2

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