### 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.

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 language | English |
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Place of Publication | Tilburg |

Publisher | Department of Econometrics |

Number of pages | 29 |

Volume | 2015-031 |

Publication status | Published - 15 Jun 2015 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2015-031 |

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### 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.