Abstract
This paper introduces a second-order differentiability smoothing technique to the classical l 1 exact penalty function for constrained optimization problems(COP). Error estimations among the optimal objective values of the nonsmooth penalty problem, the smoothed penalty problem and the original optimization problem are obtained. Based on the smoothed problem, an algorithm for solving COP is proposed and some preliminary numerical results indicate that the algorithm is quite promising.
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Acknowledgements
This work is supported by the National Natural Science Foundation of China (10971193, 11171041), the Natural Science Foundation of Zhejiang Province (Y6090063), the Natural Science Foundation of Shandong Province (ZR2010AM029) and the Science Foundation of Binzhou University (BZXYL1009).
The authors would like to thank the anonymous reviewers and the editor for giving us many valuable suggestions and comments, which help us improve this paper greatly.
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Xu, X., Meng, Z., Sun, J. et al. A second-order smooth penalty function algorithm for constrained optimization problems. Comput Optim Appl 55, 155–172 (2013). https://doi.org/10.1007/s10589-012-9504-9
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DOI: https://doi.org/10.1007/s10589-012-9504-9