Skip to Main Content

Optimization Seminar

Tuesday, October 29, 2019
10:30 AM – 12:00 PM
Sherman Hall : 148C
Title: Gaddum's test for copositivity on symmetric cones
Speaker: Michael Orlitzky

Abstract:
A real symmetric n-by-n matrix A is copositive if <Ax,x> is nonnegative for all x in the nonnegative orthant. Copositive programming has attracted much attention since Burer showed that  nonconvex quadratic programming  problems can be formulated as completely-positive programs.  Alas, the power of copositive programming is offset by its difficulty: simple questions like "is this matrix copositive?" have difficult answers. In 1958, Jerry Gaddum proposed a recursive procedure to check if a given matrix is copositive by solving a series of matrix games. It is easy to implement and conceptually simple.

The concept of copositivity can be generalized to cones other than the nonnegative orthant. If K is a proper cone, then a linear operator L is copositive on K if <L(x),x> is nonnegative for all x in K. Little is known about these operators in general. This talk will introduce  relevant concepts and propose an extension of Gaddum's test to Euclidean Jordan algebras that allows us to test for copositivity on symmetric cones.