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Weak and Strong Subgradients of Set-Valued Maps

Author

Listed:
  • Elvira Hernández

    (UNED, E.T.S.I. Industriales)

  • Luis Rodríguez-Marín

    (UNED, E.T.S.I. Industriales)

Abstract

We consider weak subgradients of a set-valued map and present a new notion of strong subgradient. We study their properties and compare our constructions and results with other developments. We give existence conditions of both types and establish several optimality conditions in terms of set optimization.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:149:y:2011:i:2:d:10.1007_s10957-010-9787-x
    DOI: 10.1007/s10957-010-9787-x
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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. Jian Wen Peng & Heung Wing Joseph Lee & Wei Dong Rong & Xin Min Yang, 2005. "Hahn-Banach theorems and subgradients of set-valued maps," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(2), pages 281-297, June.
    3. 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.
    4. 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.
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    Cited by:

    1. 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.

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