### Abstract

Original language | English |
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Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 16 |

Volume | 2012-076 |

Publication status | Published - 2012 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2012-076 |

### Fingerprint

### Keywords

- robust optimization
- general convex uncertainty regions
- linear conic optimization

### Cite this

*A New Method for Deriving Robust and Globalized Robust Solutions of Uncertain Linear Conic Optimization Problems Having General Convex Uncertainty Sets*. (CentER Discussion Paper; Vol. 2012-076). Tilburg: Operations research.

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**A New Method for Deriving Robust and Globalized Robust Solutions of Uncertain Linear Conic Optimization Problems Having General Convex Uncertainty Sets.** / Gorissen, B.L.; Ben-Tal, A.; Blanc, J.P.C.; den Hertog, D.

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

TY - UNPB

T1 - A New Method for Deriving Robust and Globalized Robust Solutions of Uncertain Linear Conic Optimization Problems Having General Convex Uncertainty Sets

AU - Gorissen, B.L.

AU - Ben-Tal, A.

AU - Blanc, J.P.C.

AU - den Hertog, D.

N1 - Pagination: 16

PY - 2012

Y1 - 2012

N2 - Abstract: We propose a new way to derive tractable robust counterparts of a linear conic optimization problem by using the theory of Beck and Ben-Tal [2] on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First, we obtain a new convex reformulation of the dual problem of a robust linear conic program, and then show how to construct the primal robust solution from the dual optimal solution. Our result allows many new uncertainty regions to be considered. We give examples of tractable uncertainty regions that were previously intractable. The results are illustrated by solving a multi-item newsvendor problem. We also propose a new globalized robust counterpart that is more flexible, and is tractable for general convex uncertainty sets and any convex distance function.

AB - Abstract: We propose a new way to derive tractable robust counterparts of a linear conic optimization problem by using the theory of Beck and Ben-Tal [2] on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First, we obtain a new convex reformulation of the dual problem of a robust linear conic program, and then show how to construct the primal robust solution from the dual optimal solution. Our result allows many new uncertainty regions to be considered. We give examples of tractable uncertainty regions that were previously intractable. The results are illustrated by solving a multi-item newsvendor problem. We also propose a new globalized robust counterpart that is more flexible, and is tractable for general convex uncertainty sets and any convex distance function.

KW - robust optimization

KW - general convex uncertainty regions

KW - linear conic optimization

M3 - Discussion paper

VL - 2012-076

T3 - CentER Discussion Paper

BT - A New Method for Deriving Robust and Globalized Robust Solutions of Uncertain Linear Conic Optimization Problems Having General Convex Uncertainty Sets

PB - Operations research

CY - Tilburg

ER -