Journal of Global Optimization

, Volume 34, Issue 2, pp 159–190

Global Optimization with Nonlinear Ordinary Differential Equations

  • Adam B. Singer
  • Paul I. Barton

DOI: 10.1007/s10898-005-7074-4

Cite this article as:
Singer, A.B. & Barton, P.I. J Glob Optim (2006) 34: 159. doi:10.1007/s10898-005-7074-4


This paper examines global optimization of an integral objective function subject to nonlinear ordinary differential equations. Theory is developed for deriving a convex relaxation for an integral by utilizing the composition result defined by McCormick (Mathematical Programming 10, 147–175, 1976) in conjunction with a technique for constructing convex and concave relaxations for the solution of a system of nonquasimonotone ordinary differential equations defined by Singer and Barton (SIAM Journal on Scientific Computing, Submitted). A fully automated implementation of the theory is briefly discussed, and several literature case study problems are examined illustrating the utility of the branch-and-bound algorithm based on these relaxations.


Convex relaxationsdynamic optimizationnonquasimonotone differential equations

Copyright information

© Springer 2006

Authors and Affiliations

  • Adam B. Singer
    • 1
  • Paul I. Barton
    • 1
  1. 1.Department of Chemical EngineeringMassachusetts Institute of TechnologyCambridgeUSA