### Abstract

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Operations research |

Volume | 2011-061 |

Publication status | Published - 2011 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2011-061 |

### Fingerprint

### Keywords

- robust optimization
- ø-divergence
- goodness-of-fit statistics

### Cite this

*Robust Solutions of Optimization Problems Affected by Uncertain Probabilities*. (CentER Discussion Paper; Vol. 2011-061). Tilburg: Operations research.

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**Robust Solutions of Optimization Problems Affected by Uncertain Probabilities.** / Ben-Tal, A.; den Hertog, D.; De Waegenaere, A.M.B.; Melenberg, B.; Rennen, G.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Robust Solutions of Optimization Problems Affected by Uncertain Probabilities

AU - Ben-Tal, A.

AU - den Hertog, D.

AU - De Waegenaere, A.M.B.

AU - Melenberg, B.

AU - Rennen, G.

PY - 2011

Y1 - 2011

N2 - In this paper we focus on robust linear optimization problems with uncertainty regions defined by ø-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on ø-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with ø-divergence uncertainty is tractable for most of the choices of ø typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multi-item newsvendor example, illustrate the relevance of the proposed approach.

AB - In this paper we focus on robust linear optimization problems with uncertainty regions defined by ø-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on ø-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with ø-divergence uncertainty is tractable for most of the choices of ø typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multi-item newsvendor example, illustrate the relevance of the proposed approach.

KW - robust optimization

KW - ø-divergence

KW - goodness-of-fit statistics

M3 - Discussion paper

VL - 2011-061

T3 - CentER Discussion Paper

BT - Robust Solutions of Optimization Problems Affected by Uncertain Probabilities

PB - Operations research

CY - Tilburg

ER -