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Improved relaxations for the parametric solutions of ODEs using differential inequalities

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  • Joseph Scott

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  • Paul Barton

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Abstract

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
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    File URL: http://hdl.handle.net/10.1007/s10898-012-9909-0
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    References listed on IDEAS

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    1. Joseph Scott & Matthew Stuber & Paul Barton, 2011. "Generalized McCormick relaxations," Journal of Global Optimization, Springer, vol. 51(4), pages 569-606, December.
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    1. repec:spr:jglopt:v:67:y:2017:i:4:d:10.1007_s10898-016-0440-6 is not listed on IDEAS

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    Keywords

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

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