Globalized Robust Optimization for Nonlinear Uncertain Inequalities

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

Research output: Working paperDiscussion paperOther research output

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Abstract

Robust optimization is a methodology that can be applied to problems that are affected by uncertainty in the problem’s parameters. The classical robust counterpart (RC) of the 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 to 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
Place of PublicationTilburg
PublisherDepartment of Econometrics
Number of pages29
Volume2015-031
Publication statusPublished - 15 Jun 2015

Publication series

NameCentER Discussion Paper
Volume2015-031

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methodology
parameter

Keywords

  • robust optimization
  • globalized robust counterpart
  • constraint violations

Cite this

Ben-Tal, A., Brekelmans, R., den Hertog, D., & Vial, J. P. (2015). Globalized Robust Optimization for Nonlinear Uncertain Inequalities. (CentER Discussion Paper; Vol. 2015-031). Tilburg: Department of Econometrics.
Ben-Tal, A. ; Brekelmans, Ruud ; den Hertog, Dick ; Vial, J.P. / Globalized Robust Optimization for Nonlinear Uncertain Inequalities. Tilburg : Department of Econometrics, 2015. (CentER Discussion Paper).
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Ben-Tal, A, Brekelmans, R, den Hertog, D & Vial, JP 2015 'Globalized Robust Optimization for Nonlinear Uncertain Inequalities' CentER Discussion Paper, vol. 2015-031, Department of Econometrics, Tilburg.

Globalized Robust Optimization for Nonlinear Uncertain Inequalities. / Ben-Tal, A.; Brekelmans, Ruud; den Hertog, Dick; Vial, J.P.

Tilburg : Department of Econometrics, 2015. (CentER Discussion Paper; Vol. 2015-031).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Globalized Robust Optimization for Nonlinear Uncertain Inequalities

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AU - Brekelmans, Ruud

AU - den Hertog, Dick

AU - Vial, J.P.

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N2 - Robust optimization is a methodology that can be applied to problems that are affected by uncertainty in the problem’s parameters. The classical robust counterpart (RC) of the 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 globalizedrobust counterpart (GRC) extends this idea by allowing controlled constraintviolations in a larger uncertainty set. The constraint violations are controlled bythe distance of the parameter to the original uncertainty set. We derive tractableGRCs that extend the initial GRCs in the literature: our GRC is applicable tononlinear constraints instead of only linear or conic constraints, and the GRCis more flexible with respect to both the uncertainty set and distance measurefunction, which are used to control the constraint violations. In addition, wepresent a GRC approach that can be used to provide an extended trade-offoverview between the objective value and several robustness measures.

AB - Robust optimization is a methodology that can be applied to problems that are affected by uncertainty in the problem’s parameters. The classical robust counterpart (RC) of the 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 globalizedrobust counterpart (GRC) extends this idea by allowing controlled constraintviolations in a larger uncertainty set. The constraint violations are controlled bythe distance of the parameter to the original uncertainty set. We derive tractableGRCs that extend the initial GRCs in the literature: our GRC is applicable tononlinear constraints instead of only linear or conic constraints, and the GRCis more flexible with respect to both the uncertainty set and distance measurefunction, which are used to control the constraint violations. In addition, wepresent a GRC approach that can be used to provide an extended trade-offoverview between the objective value and several robustness measures.

KW - robust optimization

KW - globalized robust counterpart

KW - constraint violations

M3 - Discussion paper

VL - 2015-031

T3 - CentER Discussion Paper

BT - Globalized Robust Optimization for Nonlinear Uncertain Inequalities

PB - Department of Econometrics

CY - Tilburg

ER -

Ben-Tal A, Brekelmans R, den Hertog D, Vial JP. Globalized Robust Optimization for Nonlinear Uncertain Inequalities. Tilburg: Department of Econometrics. 2015 Jun 15. (CentER Discussion Paper).