# Representing the Positive Semidefinite Cone using the Second Order Cone

Tuesday, January 17, 2017 - 4:40pm
PDL C-401

In this talk we present a recent result of Hamza Fawzi which answers the question of whether it is possible to express the general positive semidefinite cone using second-order cones. The result shows that the \$3 x 3\$ positive semidefinite cone \$S^3_+\$ does not admit a second-order cone representation. The proof relies on the method of Gouveia, Parrilo and Thomas which shows that existence of cone lifts of convex sets is equivalent to a certain factorization of the slack operator of the set. We explain how this framework is used in the paper to show that \$S^3_+\$ has no finite second order cone lift.

## Speaker

Amy Wiebe, Department of Mathematics, University of Washington