Global Methods for Dynamic Optimization and Mixed-Integer Dynamic Optimization

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• 作者：Benoî ; t Chachuat ; Adam B. Singer ; Paul I. Barton
• 刊名：Industrial & Engineering Chemistry Research
• 出版年：2006
• 出版时间：December 6, 2006
• 年：2006
• 卷：45
• 期：25
• 页码：8373 - 8392
• 全文大小：462K
• 年卷期：v.45,no.25(December 6, 2006)
• ISSN：1520-5045

文摘

An overview of global methods for dynamic optimization and mixed-integer dynamic optimization (MIDO)is presented, with emphasis placed on the control parametrization approach. These methods consist of extendingexisting continuous and mixed-integer global optimization algorithms to encompass solution of problemswith ODEs embedded. A prerequisite for so doing is a convexity theory for dynamic optimization as well asthe ability to build valid convex relaxations for Bolza-type functionals. For solving dynamic optimizationproblems globally, our focus is on the use of branch-and-bound algorithms; on the other hand, MIDO problemsare handled by adapting the outer-approximation algorithm originally developed for mixed-integer nonlinearproblems (MINLPs) to optimization problems embedding ODEs. Each of these algorithms is thoroughlydiscussed and illustrated. Future directions for research are also discussed, including the recent developmentsof general, convex, and concave relaxations for the solutions of nonlinear ODEs.