### Abstract

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

Place of Publication | Tilburg |

Publisher | Operations research |

Volume | 2011-060 |

Publication status | Published - 2011 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2011-060 |

### Fingerprint

### Keywords

- Conic Quadratic Program
- hidden convexity
- implementation error
- robust optimization
- simultaneous diagonalizability
- S-lemma

### Cite this

*Immunizing Conic Quadratic Optimization Problems Against Implementation Errors*. (CentER Discussion Paper; Vol. 2011-060). Tilburg: Operations research.

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**Immunizing Conic Quadratic Optimization Problems Against Implementation Errors.** / Ben-Tal, A.; den Hertog, D.

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

TY - UNPB

T1 - Immunizing Conic Quadratic Optimization Problems Against Implementation Errors

AU - Ben-Tal, A.

AU - den Hertog, D.

PY - 2011

Y1 - 2011

N2 - We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonalized. This extension of the S-lemma may also be useful for other purposes. We extend the result to the case in which the uncertainty region is the intersection of two convex quadratic inequalities. The robust counterpart for this case is also equivalent to a system of conic quadratic constraints. Results for convex conic quadratic constraints with implementation error are also given. We conclude with showing how the theory developed can be applied in robust linear optimization with jointly uncertain parameters and implementation errors, in sequential robust quadratic programming, in Taguchi’s robust approach, and in the adjustable robust counterpart.

AB - We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonalized. This extension of the S-lemma may also be useful for other purposes. We extend the result to the case in which the uncertainty region is the intersection of two convex quadratic inequalities. The robust counterpart for this case is also equivalent to a system of conic quadratic constraints. Results for convex conic quadratic constraints with implementation error are also given. We conclude with showing how the theory developed can be applied in robust linear optimization with jointly uncertain parameters and implementation errors, in sequential robust quadratic programming, in Taguchi’s robust approach, and in the adjustable robust counterpart.

KW - Conic Quadratic Program

KW - hidden convexity

KW - implementation error

KW - robust optimization

KW - simultaneous diagonalizability

KW - S-lemma

M3 - Discussion paper

VL - 2011-060

T3 - CentER Discussion Paper

BT - Immunizing Conic Quadratic Optimization Problems Against Implementation Errors

PB - Operations research

CY - Tilburg

ER -