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Characterizations of super efficiency in cone-convexlike vector optimization with set-valued maps

Author

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  • Wei Dong Rong
  • Yu Nan Wu

Abstract

In this paper, we extend the concept of cone-convexlikeness of single-valued maps to set-valued maps and study super efficiency in cone-convexlike vector optimization with set-valued maps. Under the assumption of the cone-convexlikeness, some characterizations of super efficiency are established in terms of the scalarization, Lagrange multipliers and super duality, respectively. Copyright Springer-Verlag Berlin Heidelberg 1998

Suggested Citation

  • Wei Dong Rong & Yu Nan Wu, 1998. "Characterizations of super efficiency in cone-convexlike vector optimization with set-valued maps," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 247-258, November.
    • Handle: RePEc:spr:mathme:v:48:y:1998:i:2:p:247-258
    DOI: 10.1007/s001860050026
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    Cited by:

    1. Z. A. Zhou & J. W. Peng, 2012. "Scalarization of Set-Valued Optimization Problems with Generalized Cone Subconvexlikeness in Real Ordered Linear Spaces," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 830-841, September.
    2. Ruchi, Arora & Lalitha, C.S., 2005. "Proximal proper efficiency in set-valued optimization," Omega, Elsevier, vol. 33(5), pages 407-411, October.
    3. Z. A. Zhou & X. M. Yang, 2011. "Optimality Conditions of Generalized Subconvexlike Set-Valued Optimization Problems Based on the Quasi-Relative Interior," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 327-340, August.
    4. M. Chinaie & J. Zafarani, 2009. "Image Space Analysis and Scalarization of Multivalued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 451-467, September.

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