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Frontiers in Global Optimization pp 83–108Cite as

A New Approach in Deterministic Global Optimisation of Problems with Ordinary Differential Equations

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Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 74))

Abstract

This paper presents an alternative approach to the deterministic global optimisation of problems with ordinary differential equations in the constraints. The algorithm uses a spatial branch-and-bound approach and a novel procedure to build convex underestimation of nonconvex problems is developed. Each nonconvex functional in the original problem is underestimated by adding a separate convex quadratic term. Two approaches are presented to compute rigorous values for the weight coefficients of the quadratic terms used to relax implicitly known state-dependent functionals. The advantages of the proposed underestimation procedure are that no new decision variables nor constraints are introduced in the relaxed problem, and that functionals with state-dependent integral terms can be directly handled. The resulting global optimisation algorithm is illustrated on several case studies which consist in parameter estimation and simple optimal control problems.

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Author information

Authors and Affiliations

  1. Laboratoire des Sciences du Génie Chimique, CNRS-ENSIC, 1 rue Grandville, B.P. 451, 54001, Nancy Cedex, France

    B. Chachuat & M. A. Latifi

Authors
  1. B. Chachuat
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  2. M. A. Latifi
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Editor information

Editors and Affiliations

  1. Princeton University, USA

    C. A. Floudas

  2. University of Florida, USA

    Panos Pardalos

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© 2004 Kluwer Academic Publishers

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Chachuat, B., Latifi, M.A. (2004). A New Approach in Deterministic Global Optimisation of Problems with Ordinary Differential Equations. In: Floudas, C.A., Pardalos, P. (eds) Frontiers in Global Optimization. Nonconvex Optimization and Its Applications, vol 74. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0251-3_5

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  • DOI: https://doi.org/10.1007/978-1-4613-0251-3_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7961-4

  • Online ISBN: 978-1-4613-0251-3

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