ABSTRACT
Optimization problems over symmetric semidefinite matrix constraints belong to the realm of semidefinite programming or semidefinite optimization. Although we mainly focus on control problems here, semidefinite programs occur in combinatorial optimization, polynomial optimization, topology optimization, and so on. In the last few decades, this research field has witnessed incredible breakthroughs in numerical tools, commercial and noncommercial software developments, and fast solution algorithms. In particular, the introduction of powerful interior point methods allow us to effectively decide about the feasibility of semidefinite programs and to determine their solutions.
