The Constant Trace Property in Noncommutative Optimization

Abstract

In this article, we show that each semidefinite relaxation of a ball-constrained noncommutative polynomial optimization problem can be cast as a semidefinite program with a constant trace matrix variable. We then demonstrate how this constant trace property can be exploited via first order numerical methods to solve efficiently the semidefinite relaxations of the noncommutative problem.

8 pages, 3 tables