Journal of Global Optimization

, Volume 33, Issue 1, pp 83–107 | Cite as

Proof of Convergence for a Global Optimization Algorithm for Problems with Ordinary Differential Equations

  • Ioannis Papamichail
  • Claire S. Adjiman


A deterministic spatial branch and bound global optimization algorithm for problems with ordinary differential equations in the constraints has been developed by Papamichail and Adjiman [A rigorous global optimization algorithm for problems with ordinary differential equations. J. Glob. Optim. 24, 1–33]. In this work, it is shown that the algorithm is guaranteed to converge to the global solution. The proof is based on showing that the selection operation is bound improving and that the bounding operation is consistent. In particular, it is shown that the convex relaxation techniques used in the algorithm for the treatment of the dynamic information ensure bound improvement and consistency are achieved.


Deterministic global optimization ordinary differential equations proof of convergence 


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© Springer 2005

Authors and Affiliations

  1. 1.Centre for Process Systems Engineering, Department of Chemical EngineeringImperial College LondonLondonUK

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