EE/AA/ME 578  Optimization and System Sciences
(a.k.a Convex Optimization and Applications)
Acknowledgement: Many thanks to
Prof. Stephen Boyd and
Prof. Lieven Vandenberghe
for the permission to use (and modify)
their course and lecture material.
Course description
This course concentrates on recognizing and solving convex optimization
problems that arise in engineering and sciences. The syllabus
includes:
 Basics of convex analysis: Convex sets, functions, and optimization
problems.
 Optimization theory: Leastsquares, linear, quadratic, geometric and
semidefinite programming, and other problems. Optimality conditions,
duality theory, and applications.
 Some optimization algorithms:
Unconstrained minimization and Newton method;
Interiorpoint methods. Only a couple of algorithms (among many existing
ones) will be covered to convey the general flavor of the methods.
 Applications:
Applications in signal processing,
control, communications, statistics, networks,
finance and economics, mechanical engineering, and circuit design
(we may focus on some applications
more than others, or skip some of them, depending on the background
and interest of the students).
 Some recent topics (time permitting):
Dual decomposition methods for decentralized
optimization; compressed sensing for sparse signals.
Course objectives:
 to give students the tools and training to recognize convex
optimization problems that arise in engineering
 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, and the background
required to use the methods in
their own research work
top of ee578 page
Basic course information
Credit: 3 units
Lectures: Tuesdays and Thursdays, 11am12:20pm, Loew Hall Room 206.
Instructor:
Maryam Fazel,
office: Paul Allen Center, Room CSE 230. Phone: (206) 6164781.
click here to send
email
Office hours: Tuesdays 2:304:30pm, or by appointment
Teaching assistant:
Xiaolong Yu, office: Room 253A, EE bldg
click here to send
email
TA office hours:Mondays 56pm, and Wednesdays 46pm
Textbook and optional references: The main textbook is
Also, printed copies are available for sale at the UW Bookstore.
Optional books that serve as secondary reference texts:
 A. BenTal and A. Nemirovski, Lectures on Modern Convex
Optimization: Analysis, Algorithms, and Engineering Applications.
MPS/SIAM Series on Optimization.
 D. Bertsekas, A. Nedic, A. Ozdaglar, Convex Analysis and
Optimization. Athena Scientific.
 J. Borwein, A. Lewis, Convex Analysis and Nonlinear Optimization:
Theory and Examples. SpringerVerlag.
 D. Luenberger, Linear and Nonlinear Programming,
AddisonWesley.
 J. Nocedal and S. Wright, Numerical Optimization,
Springer.
Course requirements:
 Weekly homework assignments (total of 8 homework sets), which
involve some MATLAB programming.
 Final exam, 24hour takehome. There will be 4 onehour time
slots for picking up the exam: March 13 (pm), March 14 (am and pm),
March 15 (am); and you should return it no later than 24 hours after pickup.
Grading: homework 60%, final 40% (approximate weights).
Prerequisites: Solid knowledge of linear algebra
and ability to program in MATLAB. Elementary analysis. Elementary
probability. Exposure to numerical computing, optimization, and application
fields helpful but not
required; applications will be kept basic and simple.
top of ee578 page
Lectures
Theory (plus lots of examples):
 Lecture #1. Introduction
(pdf file),
(2perpage pdf)
Survey sheet (please fill and return to us): (pdf file)
 Lecture #2. Convex sets
(pdf file),
(2perpage pdf)
 Lecture #3. Convex functions (Updated: 1/17/08)
(pdf file),
(2perpage pdf)
 Lecture #4. Convex optimization problems
Part 1: General
(pdf file),
(2perpage pdf)
Part 2: Linear, quadratic, geometric programming
(Updated: 1/30/08)
(pdf file),
(2perpage pdf)
Part 3: Semidefinite programming, vector optimization
(pdf file),
(2perpage pdf)
 Lecture #5. Duality (Updated: 2/13/08)
(pdf file),
(2perpage pdf)
Some applications:
Algorithms:
Videos of all lectures are available through the
EDGE webpage for the course (only during the quarter)
top of ee578 page
Software

CVX, MATLAB software for
Disciplined Convex Programming (Michael Grant, Stephen Boyd, Yinyu Ye).
A helpful
overview of CVX

SeDuMi, software for solving SDPs (Jos Sturm).

YALMIP, a parser for writing SDPs in MATLAB (Johan Lofberg).
More links
top of ee578 page
