Optimality of Affine Policies in Multi-stage Robust Optimization
Author(s)
Bertsimas, Dimitris J.; Iancu, Dan Andrei; Parillo, Pablo A.
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In this paper, we prove the optimality of disturbance-affine control policies in the context of one-dimensional, constrained, multistage robust optimization. Our results cover the finite-horizon case, with minimax (worst-case) objective, and convex state costs plus linear control costs. We develop a new proof methodology, which explores the relationship between the geometrical properties of the feasible set of solutions and the structure of the objective function. Apart from providing an elegant and conceptually simple proof technique, the approach also entails very fast algorithms for the case of piecewise-affine state costs, which we explore in connection with a classical inventory management application.
Date issued
2010-05Department
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
Mathematics of Operations Research
Publisher
Institute for Operations Research and the Management Sciences
Citation
Bertsimas, D., D. A. Iancu, and P. A. Parrilo. “Optimality of Affine Policies in Multistage Robust Optimization.” Mathematics of Operations Research 35 (2010): 363-394.
Version: Author's final manuscript
ISSN
0364-765X
1526-5471