Multivariate Nonnegative Quadratic Mappings

Zhi-Quan Luo (luozqmcmaster.ca)
Jos F. Sturm (J.F.Sturmuvt.nl)
Shuzhong Zhang (zhangse.cuhk.edu.hk)

Abstract: In this paper we study several issues related to the characterization of specific classes of multivariate quadratic mappings that are nonnegative over a given domain, with nonnegativity defined by a pre-specified conic order. In particular, we consider the set (cone) of nonnegative quadratic mappings defined with respect to the positive semidefinite 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 semidefinite program.

Keywords: Linear Matrix Inequalities, Convex Cones, Robust Optimization

Category 1: Linear, Cone and Semidefinite Programming

Citation: Technical Report SEEM2003-02, Department of Systems Engineering & Engineering Management, The Chinese University of Hong Kong

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Entry Submitted: 01/18/2003
Entry Accepted: 01/18/2003
Entry Last Modified: 01/23/2003

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