IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v61y2015i1p1-23.html
   My bibliography  Save this article

Linear equalities in blackbox optimization

Author

Abstract

The mesh adaptive direct search ( Mads) algorithm is designed for blackbox optimization problems subject to general inequality constraints. Currently, Mads does not support equalities, neither in theory nor in practice. The present work proposes extensions to treat problems with linear equalities whose expression is known. The main idea consists in reformulating the optimization problem into an equivalent problem without equalities and possibly fewer optimization variables. Several such reformulations are proposed, involving orthogonal projections, QR or SVD decompositions, as well as simplex decompositions into basic and nonbasic variables. All of these strategies are studied within a unified convergence analysis, guaranteeing Clarke stationarity under mild conditions provided by a new result on the hypertangent cone. Numerical results on a subset of the CUTEst collection are reported. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Charles Audet & Sébastien Le Digabel & Mathilde Peyrega, 2015. "Linear equalities in blackbox optimization," Computational Optimization and Applications, Springer, vol. 61(1), pages 1-23, May.
    • Handle: RePEc:spr:coopap:v:61:y:2015:i:1:p:1-23
    DOI: 10.1007/s10589-014-9708-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-014-9708-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-014-9708-2?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. Ubaldo M. García-Palomares, 2020. "Non-monotone derivative-free algorithm for solving optimization models with linear constraints: extensions for solving nonlinearly constrained models via exact penalty methods," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 599-625, October.
    2. Charles Audet & Andrew R. Conn & Sébastien Le Digabel & Mathilde Peyrega, 2018. "A progressive barrier derivative-free trust-region algorithm for constrained optimization," Computational Optimization and Applications, Springer, vol. 71(2), pages 307-329, November.
    3. S. Gratton & C. W. Royer & L. N. Vicente & Z. Zhang, 2019. "Direct search based on probabilistic feasible descent for bound and linearly constrained problems," Computational Optimization and Applications, Springer, vol. 72(3), pages 525-559, April.
    4. David W. Dreisigmeyer, 2018. "Direct Search Methods on Reductive Homogeneous Spaces," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 585-604, March.

    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:coopap:v:61:y:2015:i:1:p:1-23. 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.