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On an \(l_1\) exact penalty result for mathematical programs with vanishing constraints

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Abstract

Recently, Hoheisel et al. (Nonlinear Anal 72(5):2514–2526, 2010) proved the exactness of the classical \(l_1\) penalty function for the mathematical programs with vanishing constraints (MPVC) under the MPVC-linearly independent constraint qualification (MPVC-LICQ) and the bi-active set being empty at a local minimum \(x^*\) of MPVC. In this paper, by relaxing the two conditions in the above result, we show that the \(l_1\) penalty function is still exact at a local minimum \(x^*\) of MPVC under the MPVC-generalized pseudonormality and a new assumption. Our \(l_1\) exact penalty result includes the one of Hoheisel et al. as a special case.

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Acknowledgments

This work is supported by NNSF (Nos. 11371073, 11461015, 11361018) of China, Guangxi Natural Science Foundation (Nos. 2014GXNSFFA118001, 2015GXNSFAA139010).

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Authors and Affiliations

  1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, 541004, China

    Qingjie Hu, Jiguang Wang & Zhibin Zhu

  2. School of Mathematics and Statistics, Guangxi Normal University, Guilin, 541004, China

    Yu Chen

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  1. Qingjie Hu
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  3. Yu Chen
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  4. Zhibin Zhu
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Correspondence to Qingjie Hu.

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Hu, Q., Wang, J., Chen, Y. et al. On an \(l_1\) exact penalty result for mathematical programs with vanishing constraints. Optim Lett 11, 641–653 (2017). https://doi.org/10.1007/s11590-016-1034-4

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  • DOI: https://doi.org/10.1007/s11590-016-1034-4

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