IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v25y1977i3p435-447.html
   My bibliography  Save this article

A Characterization of Stability in Linear Programming

Author

Listed:
  • Stephen M. Robinson

    (University of Wisconsin, Madison, Wisconsin)

Abstract

We prove that a necessary and sufficient condition for the primal and dual solution sets of a solvable, finite-dimensional linear programming problem to be stable under small but arbitrary perturbations in the data of the problem is that both of these sets be bounded. The distance from any pair of solutions of the perturbed problem to the solution sets of the original problem is then bounded by a constant multiple of the norm of the perturbations. These results extend earlier work of Williams.

Suggested Citation

  • Stephen M. Robinson, 1977. "A Characterization of Stability in Linear Programming," Operations Research, INFORMS, vol. 25(3), pages 435-447, June.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:3:p:435-447
    DOI: 10.1287/opre.25.3.435
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.25.3.435
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.25.3.435?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
    ---><---

    Citations

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


    Cited by:

    1. Marcel Klatt & Axel Munk & Yoav Zemel, 2022. "Limit laws for empirical optimal solutions in random linear programs," Annals of Operations Research, Springer, vol. 315(1), pages 251-278, August.
    2. Lamb, John D. & Tee, Kai-Hong, 2012. "Resampling DEA estimates of investment fund performance," European Journal of Operational Research, Elsevier, vol. 223(3), pages 834-841.
    3. Ludwig Kuntz & Stefan Scholtes, 2000. "Measuring the Robustness of Empirical Efficiency Valuations," Management Science, INFORMS, vol. 46(6), pages 807-823, June.
    4. Giorgio & Cesare, 2018. "A Tutorial on Sensitivity and Stability in Nonlinear Programming and Variational Inequalities under Differentiability Assumptions," DEM Working Papers Series 159, University of Pavia, Department of Economics and Management.
    5. Holger Scheel & Stefan Scholtes, 2003. "Continuity of DEA Efficiency Measures," Operations Research, INFORMS, vol. 51(1), pages 149-159, February.
    6. Mark Velednitsky, 2022. "Solving $$(k-1)$$ ( k - 1 ) -stable instances of k-terminal cut with isolating cuts," Journal of Combinatorial Optimization, Springer, vol. 43(2), pages 297-311, March.
    7. Ning Zhang & Chang Fang, 2020. "Saddle point approximation approaches for two-stage robust optimization problems," Journal of Global Optimization, Springer, vol. 78(4), pages 651-670, December.
    8. M. J. Cánovas & R. Henrion & M. A. López & J. Parra, 2016. "Outer Limit of Subdifferentials and Calmness Moduli in Linear and Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 925-952, June.
    9. C. Filippi, 2004. "An Algorithm for Approximate Multiparametric Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 73-95, January.
    10. Bulat Gafarov, 2019. "Simple subvector inference on sharp identified set in affine models," Papers 1904.00111, arXiv.org, revised Jul 2024.
    11. Dupacova, Jitka & Bertocchi, Marida, 2001. "From data to model and back to data: A bond portfolio management problem," European Journal of Operational Research, Elsevier, vol. 134(2), pages 261-278, October.
    12. M. G. Fiestras-Janeiro & I. Garcia-Jurado & J. Puerto, 2000. "The Concept of Proper Solution in Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 106(3), pages 511-525, September.
    13. D. T. K. Huyen & J.-C. Yao & N. D. Yen, 2024. "Characteristic sets and characteristic numbers of matrix two-person games," Journal of Global Optimization, Springer, vol. 90(1), pages 217-241, September.

    More about this item

    Statistics

    Access and download statistics

    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:inm:oropre:v:25:y:1977:i:3:p:435-447. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.