Global Optimization with Nonlinear Ordinary Differential Equations

TitleGlobal Optimization with Nonlinear Ordinary Differential Equations
Publication TypeJournal Article
Year of Publication2006
AuthorsSinger AB, Barton PI
JournalJournal of Global Optimization
Keywordsconvex relaxations, dynamic optimization, nonquasimonotone 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) 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.