Abstract
This paper deals with the Hölder metric subregularity property of a certain constraint system in Asplund space. Using the techniques of variational analysis, its main part is devoted to establish new sufficient conditions in dual spaces for Hölder metric subregularity and estimate its modulus, which are derived in terms of coderivatives and normal cones. As an application, the results are applied to study the relationship between higher order growth condition of an unconstraint minimization problem and Hölder metric subregularity property of the related constraint system.
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The authors are grateful to the referees and editors for their helpful comments and constructive suggestions which helped us to improve the quality of this work.
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Wei Ouyang: This research was supported by the National Natural Science Foundation of the People’s Republic of China (Grant 61663049) and the Yunnan Provincial Science and Technology Research Program (Grant 2017FD070).
Binbin Zhang: This research was supported by the National Natural Science Foundation of the People’s Republic of China (Grant 11461080).
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Ouyang, W., Zhang, B. & Zhu, J. Hölder metric subregularity for constraint systems in Asplund spaces. Positivity 23, 161–175 (2019). https://doi.org/10.1007/s11117-018-0600-7
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DOI: https://doi.org/10.1007/s11117-018-0600-7