Polynomial Matrix Inequalities within Tame Geometry
arXiv:2206.03941
Abstract
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.
arXiv comment13 pages, 3 figures