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A generalization of Fenchel duality in set-valued vector optimization

Author

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  • Wen Song

Abstract

A Fenchel duality result is presented for a convex set-valued vector optimization problem under boundedness or continuity hypotheses. Copyright Springer-Verlag Berlin Heidelberg 1998

Suggested Citation

  • Wen Song, 1998. "A generalization of Fenchel duality in set-valued vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 259-272, November.
    • Handle: RePEc:spr:mathme:v:48:y:1998:i:2:p:259-272
    DOI: 10.1007/s001860050027
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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. Giovanni Crespi & Ivan Ginchev & Matteo Rocca, 2006. "First-order optimality conditions in set-valued optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 87-106, February.
    3. 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.
    4. C. R. Chen & S. J. Li, 2009. "Different Conjugate Dual Problems in Vector Optimization and Their Relations," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 443-461, March.
    5. A. Y. Azimov, 2008. "Duality for Set-Valued Multiobjective Optimization Problems, Part 1: Mathematical Programming," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 61-74, April.
    6. Li, S.J. & Chen, C.R. & Wu, S.Y., 2009. "Conjugate dual problems in constrained set-valued optimization and applications," European Journal of Operational Research, Elsevier, vol. 196(1), pages 21-32, July.
    7. Crespi Giovanni P. & Ginchev Ivan & Rocca Matteo, 2004. "First order optimality conditions in set-valued optimization," Economics and Quantitative Methods qf04010, Department of Economics, University of Insubria.
    8. 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.
    9. Nguyen Mau Nam & Gary Sandine & Nguyen Nang Thieu & Nguyen Dong Yen, 2024. "A Notion of Fenchel Conjugate for Set-Valued Mappings," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1263-1292, November.

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