Robust optimization: methodology and applications

Robust Optimization (RO) is a modeling methodology, combined with computational tools, to process optimization problems in which the data are uncertain and is only known to belong to some uncertainty set. The paper surveys the main results of RO as applied to uncertain linear, conic quadratic and se...

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Bibliographic Details
Published in:Mathematical programming 2002-05, Vol.92 (3), p.453-480
Main Authors: BEN-TAL, Aharon, NEMIROVSKI, Arkadi
Format: Article
Language:English
Subjects:
Applied sciences
Exact sciences and technology
Flows in networks. Combinatorial problems
Linear programming
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Semidefinite programming
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Summary:Robust Optimization (RO) is a modeling methodology, combined with computational tools, to process optimization problems in which the data are uncertain and is only known to belong to some uncertainty set. The paper surveys the main results of RO as applied to uncertain linear, conic quadratic and semidefinite programming. For these cases, computationally tractable robust counterparts of uncertain problems are explicitly obtained, or good approximations of these counterparts are proposed, making RO a useful tool for real-world applications. We discuss some of these applications, specifically: antenna design, truss topology design and stability analysis/synthesis in uncertain dynamic systems. We also describe a case study of 90 LPs from the NETLIB collection. The study reveals that the feasibility properties of the usual solutions of real world LPs can be severely affected by small perturbations of the data and that the RO methodology can be successfully used to overcome this phenomenon.
ISSN:0025-5610
1436-4646
DOI:10.1007/s101070100286