ACM 113
Introduction to Optimization
Fall 2007

Emmanuel Candes
300 Firestone

Office Hours: M 3-4 or by appointment

Monday, Wednesday, Friday
11-11:55 a.m.
Firestone 306






Description: The aim of this course is to introduce the main ideas of optimization theory together with modern techniques for solving convex optimization problems. Matlab will be the scientific programming language for this course. Assignments may involve a fair amount of scientific programming in matlab together with more classical exercises

Prerequisite: -
ACM 100(abc), ACM 104 (Linear algebra), or undergraduate equivalent or consent of instructor. Some programming experience or some willingless to learn. Prior knowledge of matlab not required.


  • Convex sets and convex functions
  • Convex optimization: linear programming, quadratic programming, geometric programming
  • Duality theory: Lagrange multipliers, KKT optimality conditions, saddlepoints
  • Unconstrained minimization: descent methods, gradient and steepest decent methods, Newton's method
  • Constrained minimization: equality constraints, Newton's method with equality constraints
  • Interior point methods: inequality constraints, primal-dual interior point methods, logarithmic barrier methods
The course will also develop applications in statistical estimation and approximation.


  1. Convex Optimization by Stephen Boyd and Lieven Vandenberghe, Cambridge University Press (Required)
  2. A Mathematical View of Interior-Point Methods in Convex Optimization (MPS-SIAM Series on Optimization) by James Renegar, SIAM---MPS-SIAM Series on Optimization (optional)
  3. Nonlinear Programming by Dimitri P. Bertsekas, Athena Scientific; 2nd edition (optional)
  4. Numerical Optimization by Jorge Nocedal and Stephen Wright, Springer Verlag; second edition (optional)

I will do my best to post online all the handouts given in class. Also, Sheila Shull (217 Firestone) is a person you can contact at any time (between 9:30am and 5pm) if you need administrative information. Her phone number is 626-395-4560.

Teaching Assistant and Office Hours:

Peter Stobbe, Tuesday 4-5:30 p.m., 226 Guggenheim


Homework assignments: 60%
  • Homework will generally be distributed on Wednesdays and due in class the following Wednesday.
  • There will be about 5 assignments, and your lowest score will be dropped in the final grade.
  • Late homeworks will NOT be accepted for grading (medical emergencies excepted with proof).

    Final exam: 40%. There will be a take-home final exam.