### Abstract

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

Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 28 |

Volume | 2003-7 |

Publication status | Published - 2003 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 2003-7 |

### Fingerprint

### Keywords

- optimization
- linear programming
- models

### Cite this

*Multivariate Nonnegative Quadratic Mappings*. (CentER Discussion Paper; Vol. 2003-7). Tilburg: Operations research.

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**Multivariate Nonnegative Quadratic Mappings.** / Luo, Z-Q; Sturm, J.F.; Zhang, S.

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

TY - UNPB

T1 - Multivariate Nonnegative Quadratic Mappings

AU - Luo, Z-Q

AU - Sturm, J.F.

AU - Zhang, S.

N1 - Pagination: 28

PY - 2003

Y1 - 2003

N2 - In this paper we study several issues related to the characterization of speci c classes of multivariate quadratic mappings that are nonnegative over a given domain, with nonnegativity de ned by a pre-speci ed conic order.In particular, we consider the set (cone) of nonnegative quadratic mappings de ned with respect to the positive semide nite matrix cone, and study when it can be represented by linear matrix inequalities.We also discuss the applications of the results in robust optimization, especially the robust quadratic matrix inequalities and the robust linear programming models.In the latter application the implementational errors of the solution is taken into account, and the problem is formulated as a semide nite program.

AB - In this paper we study several issues related to the characterization of speci c classes of multivariate quadratic mappings that are nonnegative over a given domain, with nonnegativity de ned by a pre-speci ed conic order.In particular, we consider the set (cone) of nonnegative quadratic mappings de ned with respect to the positive semide nite matrix cone, and study when it can be represented by linear matrix inequalities.We also discuss the applications of the results in robust optimization, especially the robust quadratic matrix inequalities and the robust linear programming models.In the latter application the implementational errors of the solution is taken into account, and the problem is formulated as a semide nite program.

KW - optimization

KW - linear programming

KW - models

M3 - Discussion paper

VL - 2003-7

T3 - CentER Discussion Paper

BT - Multivariate Nonnegative Quadratic Mappings

PB - Operations research

CY - Tilburg

ER -