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Weak Subdifferentials for Set-Valued Mappings

Author

Listed:
  • X. J. Long

    (Chongqing Technology and Business University)

  • J. W. Peng

    (Chongqing Normal University)

  • X. B. Li

    (Chongqing JiaoTong University)

Abstract

The purpose of this paper is to study the weak subdifferential for set-valued mappings, which was introduced by Chen and Jahn (Math. Methods Oper. Res., 48:187–200, 1998). Two existence theorems of weak subgradients for set-valued mappings are obtained. Moreover, some properties of the weak subdifferential for set-valued mappings are derived. Our results improve the corresponding ones in the literature. Some examples are given to illustrate our results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:1:d:10.1007_s10957-013-0469-3
    DOI: 10.1007/s10957-013-0469-3
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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. 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.
    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. 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.
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