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On Several Types of Basic Constraint Qualifications via Coderivatives for Generalized Equations

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Abstract

In this paper, we study several types of basic constraint qualifications in terms of Clarke/Fréchet coderivatives for generalized equations. Several necessary and/or sufficient conditions are given to ensure these constraint qualifications. It is proved that basic constraint qualification and strong basic constraint qualification for convex generalized equations can be obtained by these constraint qualifications, and the existing results on constraint qualifications for the inequality system can be deduced from the given conditions in this paper. The main work of this paper is an extension of the study on constraint qualifications from inequality systems to generalized equations.

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Acknowledgements

The authors wish to thank the referees for many valuable comments which help us to improve the original presentation of this paper. The research of the first author was supported by the National Natural Science Foundations of P. R. China (Grants 11771384 and 11461080) and the Fok Ying-Tung Education Foundation (Grant 151101). The second author was partially supported by the Grant MOST 105-2115-M-039-002-MY3.

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Authors and Affiliations

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

    Zhou Wei

  2. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    Jen-Chih Yao

  3. Research Center of Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, 807, Taiwan

    Jen-Chih Yao

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  1. Zhou Wei
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  2. Jen-Chih Yao
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Correspondence to Jen-Chih Yao.

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Wei, Z., Yao, JC. On Several Types of Basic Constraint Qualifications via Coderivatives for Generalized Equations. J Optim Theory Appl 177, 106–126 (2018). https://doi.org/10.1007/s10957-018-1231-7

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  • DOI: https://doi.org/10.1007/s10957-018-1231-7

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