Globalized Robust Optimization for Nonlinear Uncertain Inequalities

Aharon Ben-Tal (), Ruud Brekelmans, Dick den Hertog () and Jean-Philippe Vial ()
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Aharon Ben-Tal: Department of Industrial Engineering and Management, Technion–Israel Institute of Technology, Haifa 32000, Israel
Dick den Hertog: Department of Econometrics and Operations Research, Tilburg University, 5000 LE Tilburg, Netherlands
Jean-Philippe Vial: Ordecsys, CH-1224, Chêne-Bougeries, Switzerland

INFORMS Journal on Computing, 2017, vol. 29, issue 2, 350-366

Abstract: Robust optimization is a methodology that can be applied to problems that are affected by uncertainty in their parameters. The classical robust counterpart of a problem requires the solution to be feasible for all uncertain parameter values in a so-called uncertainty set and offers no guarantees for parameter values outside this uncertainty set. The globalized robust counterpart (GRC) extends this idea by allowing controlled constraint violations in a larger uncertainty set. The constraint violations are controlled by the distance of the parameter from the original uncertainty set. We derive tractable GRCs that extend the initial GRCs in the literature: our GRC is applicable to nonlinear constraints instead of only linear or conic constraints, and the GRC is more flexible with respect to both the uncertainty set and distance measure function, which are used to control the constraint violations. In addition, we present a GRC approach that can be used to provide an extended trade-off overview between the objective value and several robustness measures.

Keywords: robust optimization; globalized robust counterpart; constraint violations (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:29:y:2017:i:2:p:350-366

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