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New differential properties of sup-type functions

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Abstract

In this paper, we study the directional derivative, subderivative, and subdifferential of sup-type functions without any compactness assumption on the index set. As applications, we provide an estimate of the Lipschitz modulus for sup-type functions.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044, China

    Jin-chuan Zhou

  2. Institute of Operations Research, Qufu Normal University, Qufu, 273165, China

    Chang-yu Wang

Authors
  1. Jin-chuan Zhou
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  2. Chang-yu Wang
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Correspondence to Jin-chuan Zhou.

Additional information

Supported by the National Natural Science Foundation of China (No. 10571106, 10671010)

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Zhou, Jc., Wang, Cy. New differential properties of sup-type functions. Acta Math. Appl. Sin. Engl. Ser. 25, 243–254 (2009). https://doi.org/10.1007/s10255-008-8001-5

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  • DOI: https://doi.org/10.1007/s10255-008-8001-5

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