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Equivalence between polyhedral projection, multiple objective linear programming and vector linear programming

Author

Listed:
  • Andreas Löhne

    (Friedrich Schiller University Jena)

  • Benjamin Weißing

    (Friedrich Schiller University Jena)

Abstract

Let a polyhedral convex set be given by a finite number of linear inequalities and consider the problem to project this set onto a subspace. This problem, called polyhedral projection problem, is shown to be equivalent to multiple objective linear programming. The number of objectives of the multiple objective linear program is by one higher than the dimension of the projected polyhedron. The result implies that an arbitrary vector linear program (with arbitrary polyhedral ordering cone) can be solved by solving a multiple objective linear program (i.e. a vector linear program with the standard ordering cone) with one additional objective space dimension.

Suggested Citation

  • Andreas Löhne & Benjamin Weißing, 2016. "Equivalence between polyhedral projection, multiple objective linear programming and vector linear programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(2), pages 411-426, October.
    • Handle: RePEc:spr:mathme:v:84:y:2016:i:2:d:10.1007_s00186-016-0554-0
    DOI: 10.1007/s00186-016-0554-0
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    References listed on IDEAS

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    1. Dauer, Jerald P. & Liu, Yi-Hsin, 1990. "Solving multiple objective linear programs in objective space," European Journal of Operational Research, Elsevier, vol. 46(3), pages 350-357, June.
    2. C. N. Jones & E. C. Kerrigan & J. M. Maciejowski, 2008. "On Polyhedral Projection and Parametric Programming," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 207-220, August.
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