Polynomial Matrix Inequalities within Tame Geometry

Understand

Polynomial matrix inequalities can be solved using hierarchies of convex relaxations, pioneered by Henrion and Lassere.

• In some cases, this might not be practical, and one may need to resort to methods with local convergence guarantees, whose development has been rather ad hoc, so far.
• In this paper, we explore several alternative approaches to the problem, with non-trivial guarantees available using results from tame geometry.