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Primal worst and dual best in robust vector optimization

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  • Caprari, Elisa
  • Cerboni Baiardi, Lorenzo
  • Molho, Elena

Abstract

We establish a relationship between the robust counterpart of an uncertain cone-convex vector problem and the optimistic counterpart of its uncertain dual. Along the line marked by Beck and Ben-Tal (2009) in the scalar case, we show that operating in the primal problem with a pessimistic view is equivalent to operating with an optimistic approach in its dual.

Suggested Citation

  • Caprari, Elisa & Cerboni Baiardi, Lorenzo & Molho, Elena, 2019. "Primal worst and dual best in robust vector optimization," European Journal of Operational Research, Elsevier, vol. 275(3), pages 830-838.
    • Handle: RePEc:eee:ejores:v:275:y:2019:i:3:p:830-838
    DOI: 10.1016/j.ejor.2019.01.003
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    References listed on IDEAS

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    1. Fliege, Jörg & Werner, Ralf, 2014. "Robust multiobjective optimization & applications in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 422-433.
    2. Oliveira, Carla & Antunes, Carlos Henggeler, 2007. "Multiple objective linear programming models with interval coefficients - an illustrated overview," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1434-1463, September.
    3. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    4. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2015. "Robust solutions to multi-objective linear programs with uncertain data," European Journal of Operational Research, Elsevier, vol. 242(3), pages 730-743.
    5. Ehrgott, Matthias & Ide, Jonas & Schöbel, Anita, 2014. "Minmax robustness for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 239(1), pages 17-31.
    6. Jonas Ide & Anita Schöbel, 2016. "Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 235-271, January.
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    Cited by:

    1. Han, Jun & Weber, Thomas A., 2023. "Price discrimination with robust beliefs," European Journal of Operational Research, Elsevier, vol. 306(2), pages 795-809.
    2. L. Q. Anh & T. Q. Duy & D. V. Hien, 2020. "Well-posedness for the optimistic counterpart of uncertain vector optimization problems," Annals of Operations Research, Springer, vol. 295(2), pages 517-533, December.
    3. Khoirunnisa Rohadatul Aisy Muslihin & Endang Rusyaman & Diah Chaerani, 2022. "Conic Duality for Multi-Objective Robust Optimization Problem," Mathematics, MDPI, vol. 10(21), pages 1-22, October.

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