Global Optimization with Nonlinear Ordinary Differential Equations

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) i...

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Bibliographic Details
Published inJournal of global optimization Vol. 34; no. 2; pp. 159 - 190
Main Authors Singer, Adam B., Barton, Paul I.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.02.2006
Subjects
Algorithms
Branch & bound algorithms
Differential equations
Mathematical programming
Methods
Optimization
Optimization techniques
Ordinary differential equations
Studies
Theory
Variables
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Summary: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. [PUBLICATION ABSTRACT]
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-005-7074-4