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Characterizations of the Benson Proper Efficiency for Nonconvex Vector Optimization

Author

Listed:
  • G. Y. Chen

    (Academia Sinica)

  • W. D. Rong

    (Inner Mongolia University)

Abstract

Under generalized cone-subconvexlikeness for vector-valued mappings in locally-convex Hausdorff topological vector spaces, a Gordan-form alternative theorem is derived. Some characterizations of the Benson proper efficiency under this generalized convexity are established in terms of scalarization, Lagrangian multipliers, saddle-point criterion, and duality.

Suggested Citation

  • G. Y. Chen & W. D. Rong, 1998. "Characterizations of the Benson Proper Efficiency for Nonconvex Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 365-384, August.
    • Handle: RePEc:spr:joptap:v:98:y:1998:i:2:d:10.1023_a:1022689517921
    DOI: 10.1023/A:1022689517921
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    Citations

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    Cited by:

    1. D. S. Kim & G. M. Lee & P. H. Sach, 2004. "Hartley Proper Efficiency in Multifunction Optimization," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 129-145, January.
    2. 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.
    3. M. Adán & V. Novo, 2004. "Proper Efficiency in Vector Optimization on Real Linear Spaces," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 515-540, June.
    4. 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.
    5. Ozdemir, Mujgan S. & Gasimov, Rafail N., 2004. "The analytic hierarchy process and multiobjective 0-1 faculty course assignment," European Journal of Operational Research, Elsevier, vol. 157(2), pages 398-408, September.
    6. 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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