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Exact characterization for subdifferentials of a special optimal value function

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Abstract

For a closed set S and a bounded closed convex set U in a real normed vector space, we give exact subdifferential formulas of an optimal value function \(\mathrm {I}\!\Gamma _{S|U}\) whose definition is based on the Minkowski function of U. \(\mathrm {I}\!\Gamma _{S|U}\) covers distance function and indicator function as special cases. The main contribution is dropping two important assumptions of some main results in the literature.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant Nos. 11271274, 11461058), Scientific Research Fund of Sichuan Provincial Education Department (Grant Nos. 11ZB153, 11ZA180) and Scientific Research Fund of Sichuan Minzu College(Grant Nos. 13XYZB011, 12XYZB006).

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Authors and Affiliations

  1. Department of Mathematics, Sichuan Normal University, Chengdu, 610066, Sichuan, China

    Shuqin Sun & Yiran He

  2. Department of Mathematics, Sichuan Minzu College, Kangding, 626001, Sichuan, China

    Shuqin Sun

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  1. Shuqin Sun
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  2. Yiran He
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Correspondence to Shuqin Sun or Yiran He.

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Sun, S., He, Y. Exact characterization for subdifferentials of a special optimal value function. Optim Lett 12, 519–534 (2018). https://doi.org/10.1007/s11590-017-1122-0

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  • DOI: https://doi.org/10.1007/s11590-017-1122-0

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