### Abstract

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

Pages (from-to) | 341-357 |

Journal | Management Science |

Volume | 59 |

Issue number | 2 |

Publication status | Published - 2013 |

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### Cite this

*Management Science*,

*59*(2), 341-357.

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*Management Science*, vol. 59, no. 2, pp. 341-357.

**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: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

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.

N1 - Appeared earlier as CentER Discussion Paper 2011-061

PY - 2013

Y1 - 2013

N2 - In this paper we focus on robust linear optimization problems with uncertainty regions defined by φ-divergences (for example, chi-squared, Hellinger, Kullback–Leibler). We show how uncertainty regions based on Φ-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 Φ-divergence uncertainty is tractable for most of the choices of Φ 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 φ-divergences (for example, chi-squared, Hellinger, Kullback–Leibler). We show how uncertainty regions based on Φ-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 Φ-divergence uncertainty is tractable for most of the choices of Φ 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.

M3 - Article

VL - 59

SP - 341

EP - 357

JO - Management Science

JF - Management Science

SN - 0025-1909

IS - 2

ER -