Multivariate Nonnegative Quadratic Mappings

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.