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A Semidefinite Programming approach for solving Multiobjective Linear Programming

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  • Victor Blanco
  • Justo Puerto
  • Safae El Haj Ben Ali

Abstract

Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions of Multiobjective Linear Programmes (MOLPs). However, all of them are based on active-set methods (simplex-like approaches). We present a different method, based on a transformation of any MOLP into a unique lifted Semidefinite Program (SDP), the solutions of which encode the entire set of Pareto-optimal extreme point solutions of any MOLP. This SDP problem can be solved, among other algorithms, by interior point methods; thus unlike an active set-method, our method provides a new approach to find the set of Pareto-optimal solutions of MOLP. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Victor Blanco & Justo Puerto & Safae El Haj Ben Ali, 2014. "A Semidefinite Programming approach for solving Multiobjective Linear Programming," Journal of Global Optimization, Springer, vol. 58(3), pages 465-480, March.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:3:p:465-480
    DOI: 10.1007/s10898-013-0056-z
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    References listed on IDEAS

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    1. Jörg Fliege, 2004. "Gap-free computation of Pareto-points by quadratic scalarizations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(1), pages 69-89, February.
    2. Matthias Ehrgott & Andreas Löhne & Lizhen Shao, 2012. "A dual variant of Benson’s “outer approximation algorithm” for multiple objective linear programming," Journal of Global Optimization, Springer, vol. 52(4), pages 757-778, April.
    3. Jörg Fliege, 2006. "An Efficient Interior-Point Method for Convex Multicriteria Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 825-845, November.
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    Cited by:

    1. Yarui Duan & Liguo Jiao & Pengcheng Wu & Yuying Zhou, 2022. "Existence of Pareto Solutions for Vector Polynomial Optimization Problems with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 148-171, October.
    2. Jae Hyoung Lee & Nithirat Sisarat & Liguo Jiao, 2021. "Multi-objective convex polynomial optimization and semidefinite programming relaxations," Journal of Global Optimization, Springer, vol. 80(1), pages 117-138, May.

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