Connections between duality in control theory and convex optimization

Several important problems in control theory can be reformulated as convex optimization problems. From duality theory in convex optimization, dual problems can be derived for these convex optimization problems. These dual problems can in turn be reinterpreted in control or system theoretic terms, often yielding new results or new proofs for existing results from control theory. Moreover, the most efficient algorithms for convex optimization solve the primal and dual problems simultaneously. Insight into the system-theoretic meaning of the dual problem can therefore be very helpful in developing efficient algorithms. The authors demonstrate these observations with some examples.