Data-driven robust optimization

The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis tests. The approach is flexibl...

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Vydáno v:Mathematical programming Ročník 167; číslo 2; s. 235 - 292
Hlavní autoři: Bertsimas, Dimitris, Gupta, Vishal, Kallus, Nathan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2018
Springer Nature B.V
Témata:
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Design optimization
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Nonlinear programming
Numerical Analysis
Operations research
Optimization techniques
Portfolio management
Queues
Statistical analysis
Theoretical
Uncertainty
Hypothesis testing
Robust optimization
Chance-constraints
62H15 (Multivariate Analysis: Hypothesis Testing)
80M50 (Optimization: Operations research, mathematical programming)
Data-driven optimization
ISSN:0025-5610, 1436-4646
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Shrnutí:The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis tests. The approach is flexible and widely applicable, and robust optimization problems built from our new sets are computationally tractable, both theoretically and practically. Furthermore, optimal solutions to these problems enjoy a strong, finite-sample probabilistic guarantee whenever the constraints and objective function are concave in the uncertainty. We describe concrete procedures for choosing an appropriate set for a given application and applying our approach to multiple uncertain constraints. Computational evidence in portfolio management and queueing confirm that our data-driven sets significantly outperform traditional robust optimization techniques whenever data are available.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-017-1125-8