ACM 270
Advanced Topics in Convex Optimization
Spring 2009

Emmanuel Candes
300 Firestone

Office Hours: M 3-4 or by appointment


1:15-3:45 p.m.
Guggenheim 202





Description: The main goal of this course is to expose students to modern and fundamental developments in convex optimization, a subject which has experienced tremendous growth in the last 15 years or so. On the conceptual side, emphasis will be put on semidefinite programming whose rich geometric theory and expressive power makes it suitable for a wide spectrum of important optimization problems arising in engineering and applied science. On the algorithmic side, the course will cover interior point methods for semidefinite programming but emphasis will be put on novel and efficient first-order methods for smooth and nonsmooth convex optimization which are suitable for large-scale problems.

This is an advanced topics course and students are expected to complete a (short) research project to receive credit.

Prerequisite: -
ACM 113 (First course in optimization), ACM 104 (Linear algebra), ACM 116 (Applied probability) or consent of instructor.


  • Review of basic concepts in optimization: convexity, duality theory, structured optimization programs; linear programming (LP), second-order cone programming (SOCP).
  • Semidefinite programming (SDP): linear matrix inequalities, duality in cone programming, log-barrier and primal-dual interior point methods for SDPs, applications to combinatorics (relaxation of combinatorially hard problems), structural design, robust optimization and machine learning.
  • Smooth convex optimization: optimal first-order methods (Nesterov's algorithm), complexity analysis.
  • Nonsmooth convex optimization: smooth approximations of nonsmooth functions, prox-functions, Nesterov's algorithm.
  • Mirror-descent algorithms (MDA).
  • Applications in statistics, signal and image processing, control theory...


  1. Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications by A. Ben-Tal and A. Nemirovski, MPS-SIAM Series on Optimization.
  2. Introductory Lectures on Convex Optimization: A Basic Course by Y. Nesterov, Kluwer Academic Publisher.
  3. Convex Optimization by Stephen Boyd and Lieven Vandenberghe, Cambridge University Press.

Handouts: All handouts will be posted online.

Teaching assistants and office hours: We may or may not have a TA depending on class enrollment.

Grading: The grade will be determined by a final project that students will have the freedom to select from a list according to their own interest. Students can also define their own project after communicating with the instructor.