Deriving Robust Counterparts of Nonlinear Uncertain Inequalities
AbstractAbstract: In this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support functions, conjugate functions, Fenchel duality) and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of constraints. It turns out that to do so one has to calculate the support function of the uncertainty set and the concave conjugate of the nonlinear constraint function. Conveniently, these two computations are completely independent. This approach has several advantages. First, it provides an easy structured way to construct the robust counterpart both for linear and nonlinear inequalities. Second, it shows that for new classes of uncertainty regions and for new classes of nonlinear optimization problems tractable counterparts can be derived. We also study some cases where the inequality is nonconcave in the uncertain parameters.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2012-053.
Date of creation: 2012
Date of revision:
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Web page: http://center.uvt.nl
Fenchel duality; robust counterpart; nonlinear inequality; robust optimization; support functions;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-07-14 (All new papers)
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- Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013.
"Robust Solutions of Optimization Problems Affected by Uncertain Probabilities,"
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