Multivariate Nonnegative Quadratic Mappings

Z-Q Luo, J.F. Sturm, S. Zhang

Research output: Working paperDiscussion paperOther research output

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Abstract

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.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages28
Volume2003-7
Publication statusPublished - 2003

Publication series

NameCentER Discussion Paper
Volume2003-7

Fingerprint

Quadratic Mapping
Matrix Inequality
Cone
Non-negative
Robust Optimization
Nonnegativity
Programming Model
Linear programming
Linear Inequalities
Linear Model
Class

Keywords

  • optimization
  • linear programming
  • models

Cite this

Luo, Z-Q., Sturm, J. F., & Zhang, S. (2003). Multivariate Nonnegative Quadratic Mappings. (CentER Discussion Paper; Vol. 2003-7). Tilburg: Operations research.
Luo, Z-Q ; Sturm, J.F. ; Zhang, S. / Multivariate Nonnegative Quadratic Mappings. Tilburg : Operations research, 2003. (CentER Discussion Paper).
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Luo, Z-Q, Sturm, JF & Zhang, S 2003 'Multivariate Nonnegative Quadratic Mappings' CentER Discussion Paper, vol. 2003-7, Operations research, Tilburg.

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

Tilburg : Operations research, 2003. (CentER Discussion Paper; Vol. 2003-7).

Research output: Working paperDiscussion paperOther 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

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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

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BT - Multivariate Nonnegative Quadratic Mappings

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Luo Z-Q, Sturm JF, Zhang S. Multivariate Nonnegative Quadratic Mappings. Tilburg: Operations research. 2003. (CentER Discussion Paper).