Tuesday 23 May 2006 at 14h00 in Celestijnenlaan 200 room S01.03
Nonnegative Bilinear Functions on the Cartesian Product of Lorentz Cones.
By G. Elabwabi (T.U. Delft) joint work with E. de Klerk and P. Parrilo
Let L_n be the n-dimensional second order cone . A linear map from R^m to R^n is called nonnegative bilinear map if the image of L_m under this map is contained in L_n. For any pair (n;m), the set of nonnegative bilinear maps forms a convex cone. In this talk we will study this cone and its dual. We will construct a linear matrix inequality (LMI) that describes this cone and its dual. We will prove that it is possible to optimize over this cone and its dual using semidefinite programming in polynomial time. We will also present some applications in optimization as well as in linear algebra.