IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v194y2009i2p377-389.html
   My bibliography  Save this article

Average case complexity results for a centering algorithm for linear programming problems under Gaussian distributions

Author

Listed:
  • Huhn, Petra
  • Wehlitz, Verena

Abstract

To solve linear programming problems by interior point methods an approximately centered interior point has to be known. Such a point can be found by an algorithmic approach - a so-called phase 1 algorithm or centering algorithm. For random linear programming problems distributed according to the rotation symmetry model, especially with normal distribution, we present probabilistic results on the quality of the origin as starting point and the average number of steps of a centering algorithm.

Suggested Citation

  • Huhn, Petra & Wehlitz, Verena, 2009. "Average case complexity results for a centering algorithm for linear programming problems under Gaussian distributions," European Journal of Operational Research, Elsevier, vol. 194(2), pages 377-389, April.
    • Handle: RePEc:eee:ejores:v:194:y:2009:i:2:p:377-389
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00005-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    References listed on IDEAS

    as
    1. ANSTREICHER, Kurt M., 1991. "A combined phase I - phase II scaled potential algorithm for linear programming," LIDAM Reprints CORE 972, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Shinji Mizuno & Michael J. Todd & Yinyu Ye, 1993. "On Adaptive-Step Primal-Dual Interior-Point Algorithms for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 964-981, November.
    3. Michael J. Todd, 1991. "Probabilistic Models for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 16(4), pages 671-693, November.
    4. Anstreicher, K., 1989. "A Combined Phase I - Phase Ii Scaled Potential Algorithm For Linear Programming," LIDAM Discussion Papers CORE 1989039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kurt M. Anstreicher & Jun Ji & Florian A. Potra & Yinyu Ye, 1999. "Probabilistic Analysis of an Infeasible-Interior-Point Algorithm for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 176-192, February.
    2. Freund, Robert Michael., 1989. "A potential-function reduction algorithm for solving a linear program directly from an infeasible "warm start"," Working papers 3079-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Illes, Tibor & Nagy, Marianna, 2007. "A Mizuno-Todd-Ye type predictor-corrector algorithm for sufficient linear complementarity problems," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1097-1111, September.
    4. Sturm, J.F., 2002. "Implementation of Interior Point Methods for Mixed Semidefinite and Second Order Cone Optimization Problems," Other publications TiSEM b25faf5d-0142-4e14-b598-a, Tilburg University, School of Economics and Management.
    5. F. A. Potra & R. Sheng, 1998. "Superlinearly Convergent Infeasible-Interior-Point Algorithm for Degenerate LCP," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 249-269, May.
    6. Yaguang Yang, 2013. "A Polynomial Arc-Search Interior-Point Algorithm for Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 859-873, September.
    7. G. Y. Zhao, 1999. "Interior-Point Methods with Decomposition for Solving Large-Scale Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 169-192, July.
    8. Zs. Darvay & T. Illés & B. Kheirfam & P. R. Rigó, 2020. "A corrector–predictor interior-point method with new search direction for linear optimization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(3), pages 1123-1140, September.
    9. Soodabeh Asadi & Hossein Mansouri & Zsolt Darvay & Maryam Zangiabadi & Nezam Mahdavi-Amiri, 2019. "Large-Neighborhood Infeasible Predictor–Corrector Algorithm for Horizontal Linear Complementarity Problems over Cartesian Product of Symmetric Cones," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 811-829, March.
    10. M. Salahi & T. Terlaky, 2007. "Adaptive Large-Neighborhood Self-Regular Predictor-Corrector Interior-Point Methods for Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 143-160, January.
    11. Yinyu Ye, 2005. "A New Complexity Result on Solving the Markov Decision Problem," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 733-749, August.
    12. Maziar Salahi & Renata Sotirov & Tamás Terlaky, 2004. "On self-regular IPMs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(2), pages 209-275, December.
    13. Y. B. Zhao & J. Y. Han, 1999. "Two Interior-Point Methods for Nonlinear P *(τ)-Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 659-679, September.
    14. Potra, Florian A., 2002. "The Mizuno-Todd-Ye algorithm in a larger neighborhood of the central path," European Journal of Operational Research, Elsevier, vol. 143(2), pages 257-267, December.
    15. M. Sayadi Shahraki & H. Mansouri & M. Zangiabadi, 2017. "Two wide neighborhood interior-point methods for symmetric cone optimization," Computational Optimization and Applications, Springer, vol. 68(1), pages 29-55, September.
    16. Mehdi Karimi & Levent Tunçel, 2020. "Primal–Dual Interior-Point Methods for Domain-Driven Formulations," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 591-621, May.
    17. M. Sayadi Shahraki & H. Mansouri & M. Zangiabadi, 2016. "A New Primal–Dual Predictor–Corrector Interior-Point Method for Linear Programming Based on a Wide Neighbourhood," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 546-561, August.
    18. Wadhwa, Hitendra K. S. (Hitendra Kumar Singh) & Freund, Robert Michael., 1992. "Implementation and combined empirical study of combined Phase I-Phase II potential reduction algorithm for linear programming," Working papers 3411-92., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    19. Behrouz Kheirfam, 2014. "A New Complexity Analysis for Full-Newton Step Infeasible Interior-Point Algorithm for Horizontal Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 853-869, June.
    20. Behrouz Kheirfam, 2015. "A Corrector–Predictor Path-Following Method for Convex Quadratic Symmetric Cone Optimization," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 246-260, January.

    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:eee:ejores:v:194:y:2009:i:2:p:377-389. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.