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On Polyhedral Projection and Parametric Programming

Author

Listed:
  • C. N. Jones

    (ETH Zurich)

  • E. C. Kerrigan

    (Imperial College London)

  • J. M. Maciejowski

    (University of Cambridge)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:138:y:2008:i:2:d:10.1007_s10957-008-9384-4
    DOI: 10.1007/s10957-008-9384-4
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    Cited by:

    1. Jiang, Yunpeng & Ren, Zhouyang & Lu, Chunhao & Li, Hui & Yang, Zhixue, 2024. "A region-based low-carbon operation analysis method for integrated electricity-hydrogen-gas systems," Applied Energy, Elsevier, vol. 355(C).
    2. 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.
    3. Victor V. Podinovski & Robert G. Chambers & Kazim Baris Atici & Iryna D. Deineko, 2016. "Marginal Values and Returns to Scale for Nonparametric Production Frontiers," Operations Research, INFORMS, vol. 64(1), pages 236-250, February.
    4. Yifan, Zhou & Wei, Hu & Le, Zheng & Yong, Min & Lei, Chen & Zongxiang, Lu & Ling, Dong, 2020. "Power and energy flexibility of district heating system and its application in wide-area power and heat dispatch," Energy, Elsevier, vol. 190(C).

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