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A general approach for studying duality in multiobjective optimization

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  • Radu Boţ
  • Sorin-Mihai Grad
  • Gert Wanka

Abstract

A general duality framework in convex multiobjective optimization is established using the scalarization with K-strongly increasing functions and the conjugate duality for composed convex cone-constrained optimization problems. Other scalarizations used in the literature arise as particular cases and the general duality is specialized for some of them, namely linear scalarization, maximum (-linear) scalarization, set scalarization, (semi)norm scalarization and quadratic scalarization. Copyright Springer-Verlag 2007

Suggested Citation

  • Radu Boţ & Sorin-Mihai Grad & Gert Wanka, 2007. "A general approach for studying duality in multiobjective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 417-444, June.
    • Handle: RePEc:spr:mathme:v:65:y:2007:i:3:p:417-444
    DOI: 10.1007/s00186-006-0125-x
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    References listed on IDEAS

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    1. J. B. G. Frenk & G. Kassay, 1999. "On Classes of Generalized Convex Functions, Gordan–Farkas Type Theorems, and Lagrangian Duality," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 315-343, August.
    2. E. Miglierina & E. Molho, 2002. "Scalarization and Stability in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 657-670, September.
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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.
    2. Nguyen Dinh & Dang Hai Long, 2022. "A Perturbation Approach to Vector Optimization Problems: Lagrange and Fenchel–Lagrange Duality," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 713-748, August.

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