Globalized robust optimization for nonlinear uncertain inequalities

A. Ben-Tal, Ruud Brekelmans, Dick den Hertog, J.P. Vial

Research output: Contribution to journalArticleScientificpeer-review

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.
Original languageEnglish
Pages (from-to)350-366
JournalINFORMS Journal on Computing
Volume29
Issue number2
DOIs
Publication statusPublished - Apr 2017

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Uncertainty
Robust optimization
Violations
Distance measure
Trade-offs
Methodology
Robustness
Guarantee

Keywords

  • robust optimization
  • globalized robust counterpart
  • constraint violations

Cite this

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Globalized robust optimization for nonlinear uncertain inequalities. / Ben-Tal, A.; Brekelmans, Ruud; den Hertog, Dick; Vial, J.P.

In: INFORMS Journal on Computing, Vol. 29, No. 2, 04.2017, p. 350-366.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Brekelmans, Ruud

AU - den Hertog, Dick

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AB - 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.

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