Convex relaxations in circuits, systems, and control

It is well known that a large variety of systems and control problems can be formulated as optimization problems. The classical approach pursued in typical contexts is to look for a closed form solution to the specific optimization problem at hand. The last decade has seen a noticeable shift in the meaning of "closed form" solution. The formidable increase of computational power has dramatically changed the feeling of theoreticians as well as of practitioners about what is meant by "tractable" and "untractable" problems. One of the main issues is convexity. While from a mathematical viewpoint there has been a large amount of work in the direction of "convexifying" nonconvex problems and studying structural features of convex problems, considerable advances on techniques for recognizing convexity and algorithms for solving convex problems have been made mainly in the last 15 years 1, 2]. Efforts in this direction are motivated by the recognition that a large number of engineering problems can be formulated as convex problems.