BibTeX
@MISC{Ben-tal_robustoptimization,
author = {Aharon Ben-tal and Arkadi Nemirovski},
title = {Robust Optimization — Methodology and Applications 1},
year = {}
}
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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. AMS 1991 subject classification. Primary: 90C05, 90C25, 90C30. OR/MS subject classification. Primary: Programming/Convex. Key words. Convex optimization, data uncertainty, robustness, linear programming, quadratic programming,
Keyphrases
robust optimization methodology uncertain problem subject classification uncertain dynamic system linear programming robust optimization feasibility property useful tool key word semidefinite programming case study good approximation stability analysis synthesis real world lp small perturbation tractable robust counterpart netlib collection data uncertainty m subject classification optimization problem antenna design truss topology design usual solution main result computational tool convex optimization quadratic programming real-world application ro methodology
