IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v138y2008i2d10.1007_s10957-008-9384-4.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-008-9384-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-008-9384-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:138:y:2008:i:2:d:10.1007_s10957-008-9384-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.