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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Friedrich Schiller University Jena, 07737, Jena, Germany

    Andreas Löhne & Benjamin Weißing

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  1. Andreas Löhne
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  2. Benjamin Weißing
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Correspondence to Andreas Löhne.

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Löhne, A., Weißing, B. Equivalence between polyhedral projection, multiple objective linear programming and vector linear programming. Math Meth Oper Res 84, 411–426 (2016). https://doi.org/10.1007/s00186-016-0554-0

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  • DOI: https://doi.org/10.1007/s00186-016-0554-0

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