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Duality for Set-Valued Multiobjective Optimization Problems, Part 1: Mathematical Programming

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  • A. Y. Azimov

    (Yildiz Technical University)

Abstract

The duality of multiobjective problems is studied with the help of the apparatus of conjugate set-valued mappings introduced by the author. In this paper (Part 1), a duality theory is developed for set-valued mappings, which is then used to derive dual relations for some general multiobjective optimization problems which include convex programming and optimal control problems. Using this result, in the companion paper (Part 2), duality theorems are proved for multiobjective quasilinear and linear optimal control problems. The theory is applied to get dual relations for some multiobjective optimal control problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:1:d:10.1007_s10957-007-9313-y
    DOI: 10.1007/s10957-007-9313-y
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    References listed on IDEAS

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    1. Hidefumi Kawasaki, 1982. "A Duality Theorem in Multiobjective Nonlinear Programming," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 95-110, February.
    2. X. X. Huang & X. Q. Yang, 2004. "Duality for Multiobjective Optimization via Nonlinear Lagrangian Functions," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 111-127, January.
    3. Shelby Brumelle, 1981. "Duality for Multiple Objective Convex Programs," Mathematics of Operations Research, INFORMS, vol. 6(2), pages 159-172, May.
    4. X. X. Huang & X. Q. Yang, 2001. "Duality and Exact Penalization for Vector Optimization via Augmented Lagrangian," Journal of Optimization Theory and Applications, Springer, vol. 111(3), pages 615-640, December.
    5. 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.
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    Cited by:

    1. Refail Kasimbeyli & Masoud Karimi, 2021. "Duality in nonconvex vector optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 139-160, May.

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