N&O lecture: Frank Permenter (MIT)

Everyone is very welcome to attend the CWI lecture of Frank Permenter (MIT) with the title: Dimension Reduction For SDPs Via Jordan Algebras.

Abstract:
We propose a new method for simplifying semidefinite programs inspired by symmetry reduction. Specifically, we show if a projection satisfies certain invariance conditions, restricting to its range yields an equivalent primal-dual pair over a lower-dimensional symmetric cone-namely, the cone-of-squares of a Jordan subalgebra of symmetric matrices.  We then give a simple algorithm for minimizing the rank of this projection and hence the dimension of this cone. Finally, we explore connections with *-algebra-based reduction methods, which, along with symmetry reduction, can be seen as special cases of our method. Joint work with Pablo Parrilo.