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Global Optimization with Nonlinear Ordinary Differential Equations

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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.

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Singer, A.B., Barton, P.I. Global Optimization with Nonlinear Ordinary Differential Equations. J Glob Optim 34, 159–190 (2006). https://doi.org/10.1007/s10898-005-7074-4

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