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Journal of Optimization Theory and Applications

, Volume 138, Issue 2, pp 207–220 | Cite as

On Polyhedral Projection and Parametric Programming

  • C. N. Jones
  • E. C. Kerrigan
  • J. M. Maciejowski
Article

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.

Keywords

Parametric programming Polyhedral projection Computational geometry 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • C. N. Jones
    • 1
  • E. C. Kerrigan
    • 2
  • J. M. Maciejowski
    • 3
  1. 1.Automatic Control LaboratoryETH ZurichZurichSwitzerland
  2. 2.Department of Aeronautics and Department of Electrical and Electronic EngineeringImperial College LondonLondonUK
  3. 3.Department of EngineeringUniversity of CambridgeCambridgeUK

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