A Geometric Characterization of the Power of Finite Adaptability in Multistage Stochastic and Adaptive Optimization
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Bertsimas_A Geometric Characterization.pdf
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Author(s)
Goyal, Vineet
Sun, Xu Andy
Bertsimas, Dimitris J
Date Issued
February 2011
Journal
Mathematics of Operations Research
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Bertsimas, D., V. Goyal, and X. A. Sun. “A Geometric Characterization of the Power of Finite Adaptability in Multistage Stochastic and Adaptive Optimization.” Mathematics of Operations Research 36.1 (2011): 24–54.
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Author's final manuscript
Abstract
In this paper, we show a significant role that geometric properties of uncertainty sets, such as symmetry, play in determining the power of robust and finitely adaptable solutions in multistage stochastic and adaptive optimization problems. We consider a fairly general class of multistage mixed integer stochastic and adaptive optimization problems and propose a good approximate solution policy with performance guarantees that depend on the geometric properties of the uncertainty sets. In particular, we show that a class of finitely adaptable solutions is a good approximation for both the multistage stochastic and the adaptive optimization problem. A finitely adaptable solution generalizes the notion of a static robust solution and specifies a small set of solutions for each stage; the solution policy implements the best solution from the given set, depending on the realization of the uncertain parameters in past stages. Therefore, it is a tractable approximation to a fully adaptable solution for the multistage problems. To the best of our knowledge, these are the first approximation results for the multistage problem in such generality. Moreover, the results and the proof techniques are quite general and also extend to include important constraints such as integrality and linear conic constraints.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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DOI of Published Version
https://doi.org/10.1287/moor.1110.0482
