IDEAS home Printed from
   My bibliography  Save this article

Improved relaxations for the parametric solutions of ODEs using differential inequalities


  • Joseph Scott


  • Paul Barton



A new method is described for computing nonlinear convex and concave relaxations of the solutions of parametric ordinary differential equations (ODEs). Such relaxations enable deterministic global optimization algorithms to be applied to problems with ODEs embedded, which arise in a wide variety of engineering applications. The proposed method computes relaxations as the solutions of an auxiliary system of ODEs, and a method for automatically constructing and numerically solving appropriate auxiliary ODEs is presented. This approach is similar to two existing methods, which are analyzed and shown to have undesirable properties that are avoided by the new method. Two numerical examples demonstrate that these improvements lead to significantly tighter relaxations than previous methods. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Joseph Scott & Paul Barton, 2013. "Improved relaxations for the parametric solutions of ODEs using differential inequalities," Journal of Global Optimization, Springer, vol. 57(1), pages 143-176, September.
  • Handle: RePEc:spr:jglopt:v:57:y:2013:i:1:p:143-176
    DOI: 10.1007/s10898-012-9909-0

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

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

    References listed on IDEAS

    1. Joseph Scott & Matthew Stuber & Paul Barton, 2011. "Generalized McCormick relaxations," Journal of Global Optimization, Springer, vol. 51(4), pages 569-606, December.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. repec:spr:jglopt:v:73:y:2019:i:1:d:10.1007_s10898-018-0691-5 is not listed on IDEAS
    2. repec:spr:joptap:v:162:y:2014:i:1:d:10.1007_s10957-013-0426-1 is not listed on IDEAS
    3. repec:spr:jglopt:v:67:y:2017:i:4:d:10.1007_s10898-016-0440-6 is not listed on IDEAS
    4. repec:spr:joptap:v:163:y:2014:i:2:d:10.1007_s10957-014-0539-1 is not listed on IDEAS

    More about this item


    Convex relaxations; Global optimization; Optimal control; 34A40; 65L05; 49M20; 49M37; 90C26;

    JEL classification:


    Access and download statistics


    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:jglopt:v:57:y:2013:i:1:p:143-176. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.