Optimality of Affine Policies in Multi-stage Robust Optimization
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MOR_robust.pdf
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513.66 KB
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Author(s)
Bertsimas, Dimitris J.
Iancu, Dan Andrei
Parillo, Pablo A.
Date Issued
May 2010
Journal
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
Abstract
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.
MIT Department
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 Management
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1287/moor.1100.0444
