Journal
JOURNAL OF GLOBAL OPTIMIZATION
Volume 34, Issue 2, Pages 159-190Publisher
SPRINGER
DOI: 10.1007/s10898-005-7074-4
Keywords
convex relaxations; dynamic optimization; nonquasimonotone differential equations
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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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