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On Polyhedral Projection and Parametric Programming

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Abstract

This paper brings together two fundamental topics: polyhedral projection and parametric linear programming. First, it is shown that, given a parametric linear program (PLP), a polyhedron exists whose projection provides the solution to the PLP. Second, the converse is tackled and it is shown how to formulate a PLP whose solution is the projection of an appropriately defined polyhedron described as the intersection of a finite number of halfspaces. The input to one operation can be converted to an input of the other operation and the resulting output can be converted back to the desired form in polynomial time—this implies that algorithms for computing projections or methods for solving parametric linear programs can be applied to either problem class.

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Authors and Affiliations

  1. Automatic Control Laboratory, ETH Zurich, Physikstrasse 3, Zurich, Switzerland

    C. N. Jones

  2. Department of Aeronautics and Department of Electrical and Electronic Engineering, Imperial College London, Exhibition Road, London, SW7 2AZ, UK

    E. C. Kerrigan

  3. Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK

    J. M. Maciejowski

Authors
  1. C. N. Jones
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  2. E. C. Kerrigan
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  3. J. M. Maciejowski
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Correspondence to C. N. Jones.

Additional information

Communicated by D.Q. Mayne.

E.C. Kerrigan’s research was supported in part by the Royal Academy of Engineering, UK.

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Jones, C.N., Kerrigan, E.C. & Maciejowski, J.M. On Polyhedral Projection and Parametric Programming. J Optim Theory Appl 138, 207–220 (2008). https://doi.org/10.1007/s10957-008-9384-4

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  • DOI: https://doi.org/10.1007/s10957-008-9384-4

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