Global Optimization with Nonlinear Ordinary Differential Equations

  • Authors:

  • Adam B. Singer;Paul I. Barton

  • Affiliations:

  • Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, USA;Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, USA

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2006

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Abstract

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.