A hierarchy of policies for adaptive optimization
Author(s)
Iancu, Dan Andrei; Parrilo, Pablo A.; Bertsimas, Dimitris J
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Alternative title
A Hierarchy of Near-Optimal Policies for Multistage Adaptive Optimization
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In this paper, we propose a new tractable framework for dealing with linear dynamical systems affected by uncertainty, applicable to multistage robust optimization and stochastic programming. We introduce a hierarchy of near-optimal polynomial disturbance-feedback control policies, and show how these can be computed by solving a single semidefinite programming problem. The approach yields a hierarchy parameterized by a single variable (the degree of the polynomial policies), which controls the trade-off between the optimality gap and the computational requirements. We evaluate our framework in the context of three classical applications-two in inventory management, and one in robust regulation of an active suspension system-in which very strong numerical performance is exhibited, at relatively modest computational expense.
Date issued
2011-08Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems; Massachusetts Institute of Technology. Operations Research Center; Sloan School of ManagementJournal
IEEE Transactions on Automatic Control
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Bertsimas, Dimitris, Dan Andrei Iancu, and Pablo A. Parrilo. “A Hierarchy of Near-Optimal Policies for Multistage Adaptive Optimization.” IEEE Transactions on Automatic Control 56.12 (2011): 2809–2824.
Version: Author's final manuscript
ISSN
0018-9286
1558-2523