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On generalized \(\epsilon \)-subdifferential and radial epiderivative of set-valued mappings

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Abstract

In this paper, a generalized \(\epsilon \)-subdifferential, which was defined by the radial epiderivative and a norm, is first introduced for a set-valued mapping. Some existence theorems of the generalized \(\epsilon \)-subdifferential and the radial epiderivative are discussed. A relationship between the existence of the radial epiderivative and the existence of the generalized \(\epsilon \)-subdifferential is investigated for a set-valued mapping.

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Acknowledgments

This research was partially supported by the National Natural Science Foundation of China (Grant Number: 10871216) and Chongqing University Postgraduates Science and Innovation Fund (Grant Number: CDJXS11 1000 22).

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Authors and Affiliations

  1. Department of Science, Henan Institute of Engineering, Zhengzhou, 451191, China

    X. L. Guo & Z. W. Li

  2. Henan Institute of Engineering, Zhengzhou, 451191, China

    C. J. Zhao

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  1. X. L. Guo
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  2. C. J. Zhao
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  3. Z. W. Li
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Correspondence to X. L. Guo.

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Guo, X.L., Zhao, C.J. & Li, Z.W. On generalized \(\epsilon \)-subdifferential and radial epiderivative of set-valued mappings. Optim Lett 8, 1707–1720 (2014). https://doi.org/10.1007/s11590-013-0691-9

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  • DOI: https://doi.org/10.1007/s11590-013-0691-9

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