Convex Optimization

What you will learn

• How to recognize convex optimization problems that arise in applications.
• How to present the basic theory of such problems, concentrating on results that are useful in computation.
• A thorough understanding of how such problems are solved, and some experience in solving them.
• The background required to use the methods in your own research work or applications.

Program Overview

This course concentrates on recognizing and solving convex optimization problems that arise in applications. The syllabus includes: 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.

This course should benefit anyone who uses or will use scientific computing or optimization in engineering or related work (e.g., machine learning, finance). More specifically, people from the following fields: Electrical Engineering (especially areas like signal and image processing, communications, control, EDA & CAD); Aero & Astro (control, navigation, design), Mechanical & Civil Engineering (especially robotics, control, structural analysis, optimization, design); Computer Science (especially machine learning, robotics, computer graphics, algorithms & complexity, computational geometry); Operations Research; Scientific Computing and Computational Mathematics. The course may be useful to students and researchers in several other fields as well: Mathematics, Statistics, Finance, Economics.

Additional Instructors / Contributors

Neal Parikh

Neal Parikh is a 5th year Ph.D. Candidate in Computer Science at Stanford University. He has previously taught Convex Optimization (EE 364A) at Stanford University and holds a B.A.S., summa cum laude, in Mathematics and Computer Science from the University of Pennsylvania and an M.S. in Computer Science from Stanford University.

Ernest Ryu

Ernest Ryu is a PhD candidate in Computational and Mathematical Engineering at Stanford University. He has served as a TA for EE364a at Stanford. His research interested include stochastic optimization, convex analysis, and scientific computing.

Madeleine Udell

Madeleine Udell is a PhD candidate in Computational and Mathematical Engineering at Stanford University. She has served as a TA and as an instructor for EE364a at Stanford. Her research applies convex optimization techniques to a variety of non-convex applications, including sigmoidal programming, biconvex optimization, and structured reinforcement learning problems, with applications to political science, biology, and operations research.