Abstract
In previous papers [17,18], we have described an algorithm for globally solving dynamic optimization problems with integral objective functions subject to ordinary differential equations. The method employs a branch-and-bound algorithm on a Euclidean space utilizing convex relaxations of the dynamic optimization problem. We show that convex relaxations for an integrand pointwise in time imply convex relaxations for an integral. The integrand is treated as a function only of the parameters (and time) known only by composition with the solution of the embedded nonlinear differential equations. Combining the composition technique attributed to McCormick, differential inequalities, and a novel outer approximation technique, convex relaxations for the integrand are derived. This paper addresses the concepts from a tutorial perspective.
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Singer, A.B., Barton, P.I. (2004). Global Solution of Optimization Problems with Dynamic Systems Embedded. In: Floudas, C.A., Pardalos, P. (eds) Frontiers in Global Optimization. Nonconvex Optimization and Its Applications, vol 74. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0251-3_26
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DOI: https://doi.org/10.1007/978-1-4613-0251-3_26
Publisher Name: Springer, Boston, MA
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