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∊-Strictly Efficient Solutions Of Vector Optimization Problems With Set-Valued Maps

Author

Listed:
  • TAIYONG LI

    (Department of Mathematics, Nanchang University, Nanchang 330031, China)

  • YIHONG XU

    (Department of Mathematics, Nanchang University, Nanchang 330031, China)

  • CHUANXI ZHU

    (Department of Mathematics, Nanchang University, Nanchang 330031, China)

Abstract

In this paper, the notion of ∊-strictly efficient solution for vector optimization with set-valued maps is introduced. Under the assumption of the ic-cone-convexlikeness for set-valued maps, the scalarization theorem, ∊-Lagrangian multiplier theorem, ∊-saddle point theorems and ∊-duality assertions are established for ∊-strictly efficient solution.

Suggested Citation

  • Taiyong Li & Yihong Xu & Chuanxi Zhu, 2007. "∊-Strictly Efficient Solutions Of Vector Optimization Problems With Set-Valued Maps," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(06), pages 841-854.
    • Handle: RePEc:wsi:apjorx:v:24:y:2007:i:06:n:s0217595907001577
    DOI: 10.1142/S0217595907001577
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    Citations

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    Cited by:

    1. 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.
    2. Zhi-Ang Zhou & Xin-Min Yang, 2014. "Scalarization of $$\epsilon $$ ϵ -Super Efficient Solutions of Set-Valued Optimization Problems in Real Ordered Linear Spaces," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 680-693, August.
    3. M. Chinaie & J. Zafarani, 2013. "Image Space Analysis and Scalarization for ε-Optimization of Multifunctions," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 685-695, June.

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