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Lagrangian Duality for Minimization of Nonconvex Multifunctions

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  • W. Song

    (Harbin Normal University)

Abstract

Two alternative type theorems for nearly convexlike or * quasiconvex multifunctions are presented. They are used to derive Lagrangian conditions and duality results for vector optimization problems when the objectives and the constraints are nearly convexlike or * quasiconvex multifunctions.

Suggested Citation

  • W. Song, 1997. "Lagrangian Duality for Minimization of Nonconvex Multifunctions," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 167-182, April.
    • Handle: RePEc:spr:joptap:v:93:y:1997:i:1:d:10.1023_a:1022658019642
    DOI: 10.1023/A:1022658019642
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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. X. M. Yang & D. Li & S. Y. Wang, 2001. "Near-Subconvexlikeness in Vector Optimization with Set-Valued Functions," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 413-427, August.
    3. 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.
    4. L. Y. Xia & J. H. Qiu, 2008. "Superefficiency in Vector Optimization with Nearly Subconvexlike Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 125-137, January.

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