|Title||Global Optimization with Nonlinear Ordinary Differential Equations|
|Publication Type||Journal Article|
|Year of Publication||2006|
|Authors||Singer AB, Barton PI|
|Journal||Journal of Global Optimization|
|Keywords||convex 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.