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Hahn-Banach theorems and subgradients of set-valued maps

Author

Listed:
  • Jian Wen Peng
  • Heung Wing Joseph Lee
  • Wei Dong Rong
  • Xin Min Yang

Abstract

Some new results which generalize the Hahn-Banach theorem from scalar or vector-valued case to set-valued case are obtained. The existence of the Borwein-strong subgradient and Yang-weak subgradient for set-valued maps are also proven. We present a new Lagrange multiplier theorem and a new Sandwich theorem for set-valued maps. Copyright Springer-Verlag 2005

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:61:y:2005:i:2:p:281-297
    DOI: 10.1007/s001860400397
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    Cited by:

    1. 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.
    2. 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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