6.079 / 6.975 Introduction to Convex Optimization

As taught in: Fall 2009

A three-dimensional graph.

Array signal processing, with weights optimized by convex optimization. (© 2010 IEEE. Used with permission. Source: Jacob Mattingley and Stephen Boyd. "Real-Time Convex Optimization in Signal Processing." IEEE Signal Processing Magazine 27, no. 3 (2010): 50-61.)


Undergraduate / Graduate


Prof. Stephen Boyd

Prof. Pablo Parrilo

Course Features

Course Description

This course aims to give students the tools and training to recognize convex optimization problems that arise in scientific and engineering applications, presenting the basic theory, and concentrating on modeling aspects and results that are useful in applications. Topics include convex sets, convex functions, optimization problems, least-squares, linear and quadratic programs, semidefinite programming, optimality conditions, and duality theory. Applications to signal processing, control, machine learning, finance, digital and analog circuit design, computational geometry, statistics, and mechanical engineering are presented. Students complete hands-on exercises using high-level numerical software.


The course materials were developed jointly by Prof. Stephen Boyd (Stanford), who was a visiting professor at MIT when this course was taught, and Prof. Lieven Vanderberghe (UCLA).