Constrained polynomial optimization problems with noncommuting variables
Motivated by applications in control theory and systems engineering, the authors extend existing results on unconstrained polynomial optimization with noncommutating variables to the case of polydisc and ball constraints. They show that a noncommutative (nc) polynomial is nonnegative on these sets if and only if it is a sum of squares. As a consequence of this property, when solving nc polynomial optimization problems, there is need to construct a whole hierarchy of semidefinite programming (SDP) problems, optima can be obtained via a single SDP problem. This is in sharp contrast with the commutative case.
scientific article; zbMATH DE number 6081228