IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/19980003.html
   My bibliography  Save this paper

Analytic Central Path, Sensitivity Analysis and Parametric Linear Programming

Author

Listed:
  • A.G. Holder

    (University of Colorado at Denver)

  • J.F. Sturm

    (Erasmus University Rotterdam)

  • S. Zhang

    (Erasmus University Rotterdam)

Abstract

In this paper we consider properties of the central path and the analytic center of the optimalface in the context of parametric linear programming. We first show that if the right-hand sidevector of a standard linear program is perturbed, then the analytic center of the optimal face isone-side differentiable with respect to the perturbation parameter. In that case we also showthat the whole analytic central path shifts in a uniform fashion. When the objective vector isperturbed, we show that the last part of the analytic central pathis tangent to a central path defined on the optimal face of the original problem.

Suggested Citation

  • A.G. Holder & J.F. Sturm & S. Zhang, 1998. "Analytic Central Path, Sensitivity Analysis and Parametric Linear Programming," Tinbergen Institute Discussion Papers 98-003/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:19980003
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/98003.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nunez, M. A. (Manuel A.) & Freund, Robert Michael. & Massachusetts Institute of Technology. Operations Research Center., 1996. "Condition measures and properties of the central trajectory of a linear program," Working papers 316-96., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Shinji Mizuno & Michael J. Todd & Yinyu Ye, 1995. "A Surface of Analytic Centers and Primal-Dual Infeasible-Interior-Point Algorithms for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 135-162, February.
    3. Michael J. Todd, 1990. "A Dantzig-Wolfe-Like Variant of Karmarkar's Interior-Point Linear Programming Algorithm," Operations Research, INFORMS, vol. 38(6), pages 1006-1018, December.
    4. Berkelaar, A.B. & Roos, K. & Terlaky, T., 1996. "The Optimal Set and Optimal Partition Approach to Linear and Quadratic Programming," Econometric Institute Research Papers EI 9658-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. J. Frédéric Bonnans & Florian A. Potra, 1997. "On the Convergence of the Iteration Sequence of Infeasible Path Following Algorithms for Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 22(2), pages 378-407, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Zhang, S., 1998. "Global error bounds for convex conic problems," Econometric Institute Research Papers EI 9830, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

    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. Holder, A.G. & Sturm, J.F. & Zhang, S., 1998. "Analytic central path, sensitivity analysis and parametric linear programming," Econometric Institute Research Papers EI 9801, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. J.F. Sturm & S. Zhang, 1998. "On Sensitivity of Central Solutions in Semidefinite Programming," Tinbergen Institute Discussion Papers 98-040/4, Tinbergen Institute.
    3. Caron, Richard J. & Greenberg, Harvey J. & Holder, Allen G., 2002. "Analytic centers and repelling inequalities," European Journal of Operational Research, Elsevier, vol. 143(2), pages 268-290, December.
    4. Freund, Robert Michael. & Mizuno, Shinji., 1996. "Interior point methods : current status and future directions," Working papers 3924-96., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    5. Epelman, Marina A., 1973-. & Freund, Robert Michael, 1997. "Condition number complexity of an elementary algorithm for resolving a conic linear system," Working papers WP 3942-97., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    6. Zhang, S., 1998. "Global error bounds for convex conic problems," Econometric Institute Research Papers EI 9830, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Dennis Cheung & Felipe Cucker & Javier Peña, 2003. "Unifying Condition Numbers for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 609-624, November.
    8. Filiz Gurtuna & Cosmin Petra & Florian Potra & Olena Shevchenko & Adrian Vancea, 2011. "Corrector-predictor methods for sufficient linear complementarity problems," Computational Optimization and Applications, Springer, vol. 48(3), pages 453-485, April.
    9. M. Zangiabadi & G. Gu & C. Roos, 2013. "A Full Nesterov–Todd Step Infeasible Interior-Point Method for Second-Order Cone Optimization," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 816-858, September.
    10. Li-Zhi Liao, 2014. "A Study of the Dual Affine Scaling Continuous Trajectories for Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 548-568, November.

    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:tin:wpaper:19980003. 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: Tinbergen Office +31 (0)10-4088900 (email available below). General contact details of provider: https://edirc.repec.org/data/tinbenl.html .

    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.