Concentrates on recognizing and solving convex optimization problems that arise in applications. Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods. Applications to signal processing, statistics and machine learning, control and mechanical engineering, digital and analog circuit design, and finance.

to give students the tools and training to recognize convex optimization problems that arise in applications

to present the basic theory of such problems, concentrating on results that are useful in computation

to give students a thorough understanding of how such problems are solved, and some experience in solving them

to give students the background required to use the methods in their own research work or applications