Robust optimization – methodology and applications |
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Authors: | Aharon Ben-Tal Arkadi Nemirovski |
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Institution: | (1) Faculty of Industrial Engineering and Management, Technion – Israel Institute of Technology, Technion City, Haifa 32000, Israel e-mail: {morbt,nemirovs}@ie.technion.ac.il, IL |
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Abstract: | 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.
Received: May 24, 2000 / Accepted: September 12, 2001?Published online February 14, 2002 |
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Keywords: | : convex optimization – data uncertainty – robustness – linear programming – quadratic programming – semidefinite programming – engineering design – Lyapunov stability synthesis |
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