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On Subdifferentials of Set-Valued Maps

Author

Listed:
  • J. Baier

    (Universität Erlangen-Nürnberg)

  • J. Jahn

    (Universität Erlangen-Nürnberg)

Abstract

Using the concept of contingent epiderivative, we generalize the notion of subdifferential to a cone-convex set-valued map. Properties of the subdifferential are presented and an optimality condition is discussed.

Suggested Citation

  • J. Baier & J. Jahn, 1999. "On Subdifferentials of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 100(1), pages 233-240, January.
    • Handle: RePEc:spr:joptap:v:100:y:1999:i:1:d:10.1023_a:1021733402240
    DOI: 10.1023/A:1021733402240
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    References listed on IDEAS

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    1. Guang Ya Chen & Johannes Jahn, 1998. "Optimality conditions for set-valued optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 187-200, November.
    2. Johannes Jahn & Rüdiger Rauh, 1997. "Contingent epiderivatives and set-valued optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 193-211, June.
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    Cited by:

    1. Mansi Dhingra, 2019. "Henig proper subdifferential of set-valued maps," OPSEARCH, Springer;Operational Research Society of India, vol. 56(3), pages 790-805, September.
    2. Nithirat Sisarat & Rabian Wangkeeree & Tamaki Tanaka, 2020. "Sequential characterizations of approximate solutions in convex vector optimization problems with set-valued maps," Journal of Global Optimization, Springer, vol. 77(2), pages 273-287, June.
    3. Elvira Hernández & Luis Rodríguez-Marín, 2011. "Weak and Strong Subgradients of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 352-365, May.
    4. X. J. Long & J. W. Peng & X. B. Li, 2014. "Weak Subdifferentials for Set-Valued Mappings," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 1-12, July.
    5. X. L. Guo & S. J. Li, 2014. "Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 821-844, September.

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