IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v25y1983i1p39-42.html
   My bibliography  Save this article

Linear and non-linear programming software validity

Author

Listed:
  • Tolla, Pierre

Abstract

The numerical software users are often perturbed by accuracy problems imputable to the rounding errors generated by computer hardware. M. La Porte and J. Vignes (4) created the permutation-perturbation method for evaluating the validity of the solutions of linear algebraic systems, detection of the matrix singularity, and optimal termination criterion of iteratives methods. These problems exist and are considerably amplified in linear and non-linear programming algorithms using near simplex methods : Reduced Gradient of P. Wolfe and Generalized Reduced Gradient of J. Abadie (1) ; effectively, these methods proceed with a long sequence of matrix inversions which increases rounding errors, and it is not unu4sual to obtain false basic solutions or singular basic matrices. Moreover, the classical termination criterions of unconstrained optimization may involve either an untimely stop of the algorithm producing a solution far from the optimum, or, on the contrary, a large number of unprofitable iterations which does not improve the current solution. I suggest, in this paper, some quick and efficient procedures for solving these problems.

Suggested Citation

  • Tolla, Pierre, 1983. "Linear and non-linear programming software validity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 25(1), pages 39-42.
    • Handle: RePEc:eee:matcom:v:25:y:1983:i:1:p:39-42
    DOI: 10.1016/0378-4754(83)90028-9
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378475483900289
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/0378-4754(83)90028-9?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. Vignes, Jean, 1984. "An efficient implementation of optimization algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 26(3), pages 243-256.
    2. Vignes, J., 1988. "Review on stochastic approach to round-off error analysis and its applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 481-491.
    3. Alliot, Nicole, 1988. "Data error analysis in unconstrained optimization problems with the CESTAC method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 531-539.
    4. Vignes, J., 1993. "A stochastic arithmetic for reliable scientific computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(3), pages 233-261.

    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:eee:matcom:v:25:y:1983:i:1:p:39-42. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.