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A Theorem of the Alternative and Its Application to the Optimization of Set-Valued Maps

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  • Z. Li

    (Chongqing Jianzhu University)

Abstract

In this paper, we establish a theorem of the alternative in ordered linear topological spaces. Then, optimality conditions for the optimization of set-valued maps are obtained.

Suggested Citation

  • Z. Li, 1999. "A Theorem of the Alternative and Its Application to the Optimization of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 100(2), pages 365-375, February.
    • Handle: RePEc:spr:joptap:v:100:y:1999:i:2:d:10.1023_a:1021786303883
    DOI: 10.1023/A:1021786303883
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    Citations

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    Cited by:

    1. X. M. Yang & X. Q. Yang & G. Y. Chen, 2000. "Theorems of the Alternative and Optimization with Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 107(3), pages 627-640, December.
    2. Z. M. Li & M. H. Zhan, 2007. "Optimality Conditions and Lagrange Duality for Vector Extremum Problems with Set Constraint," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 323-332, December.
    3. 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.
    4. P. H. Sach, 2007. "Moreau–Rockafellar Theorems for Nonconvex Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 213-227, May.
    5. 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.
    6. Zhiang Zhou & Wenbin Wei & Fei Huang & Kequan Zhao, 2024. "Approximate weak efficiency of the set-valued optimization problem with variable ordering structures," Journal of Combinatorial Optimization, Springer, vol. 48(3), pages 1-13, October.
    7. P. H. Sach, 2003. "Nearly Subconvexlike Set-Valued Maps and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 119(2), pages 335-356, November.

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