May 31, 2011, Elings Hall 1605

This overview lecture introduces convex optimization at a high level, touching briefly on many of the topics that will be explored in more depth in later lectures. Convex optimization has emerged as a conceptually and practically useful problem class, with applications in many areas, including control system analysis and design, signal processing and communications, statistics and machine learning, finance, circuit design, wired and wireless networks, and many others. Linear and quadratic programming have been known and used since the 1950s, originally in finance and operations; new problem classes like second-order cone programming and semidefinite programming emerged only in the 1990s, originally in control systems and combinatorial optimization. In the 2000s, the use of l-1 regularization (which typically leads to a convex optimization problem) has become widespread in statistics and machine learning, as an effective method to carry out regressor selection and sparse model fitting. Over the last 5 years modeling tools like CVX and YALMIP, designed specifically for convex optimization, have dramatically improved our ability to rapidly form and solve small and medium sized convex problems, and have contributed to the rapid spread of convex optimization based applications. In 2010 the first code generator for convex optimization was developed, opening the door to rapid development of embedded applications. At the same time, the emergence of enormous data sets and cloud computing has renewed interest in distributed convex optimization for extremely large-scale problems.

Stephen P. Boyd is the Samsung Professor of Engineering, and Professor of Electrical Engineering in the Information Systems Laboratory at Stanford University. He also has a courtesy appointment in the Department of Management Science and Engineering, and is member of the Institute for Computational and Mathematical Engineering. His current research focus is on convex optimization applications in control, signal processing, and circuit design.