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On metric subregularity for convex constraint systems by primal equivalent conditions

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Abstract

In this paper, we mainly study metric subregularity for a convex constraint system defined by a convex set-valued mapping and a convex constraint subset. The main work is to provide several primal equivalent conditions for metric subregularity by contingent cone and graphical derivative. Further it is proved that these primal equivalent conditions can characterize strong basic constraint qualification of convex constraint system given by Zheng and Ng (SIAM J Optim 18:437–460, 2007).

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Acknowledgments

The authors wish to thank two anonymous referees for their many valuable comments and suggestions which help us to improve the original presentation of this paper and draw our attentions to references [12, 16].

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Authors and Affiliations

  1. School of Mathematics and Information Science, Qujing Normal University, Qujing, 655011, Yunnan, People’s Republic of China

    Liyun Huang

  2. Department of Mathematics, Yunnan University, Kunming, 650091, People’s Republic of China

    Zhou Wei

Authors
  1. Liyun Huang
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  2. Zhou Wei
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Correspondence to Zhou Wei.

Additional information

This research was supported by the National Natural Science Foundation of P. R. China (Grant 11401518), the Fok Ying-Tung Education Foundation (Grant 151101) and the Scientific Research Foundation from Education Department of Yunnan Province under Grant 2015Z009.

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Huang, L., Wei, Z. On metric subregularity for convex constraint systems by primal equivalent conditions. Optim Lett 11, 1713–1728 (2017). https://doi.org/10.1007/s11590-016-1089-2

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  • DOI: https://doi.org/10.1007/s11590-016-1089-2

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