This course discusses basic convex analysis (convex sets, functions, and optimization problems), optimization theory (linear, quadratic, semidefinite, and geometric programming; optimality conditions and duality theory), some optimization algorithms (descent methods and interior-point methods), basic applications (in signal processing, machine learning, statistics, control, communications, networks, circuit design, mechanical engineering, and finance, etc), and some advanced topics (distributed decomposition, exact convex relaxation, and parsimonious recovery, if time permits). The objective is to give students the theoretical tools and training to recognize and formulate convex optimization problems that arise in engineering and applied science as well as the understanding of how such problems are solved, and to give students the background required to use the tools and methods of optimization in their own applications and researches.
Lijun Chen (firstname.lastname@example.org)
Office hours: TUE 10:00AM-12:00PM
Office: ECOT335; Ext. 4384
S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. (This book is available on-line, but I strongly recommend to buy a hardcopy).
Optional or Other References
D. Bertsekas, A. Nedic, and A. Ozdaglar, Convex Analysis and Optimization, Athena Scientific, 2003.
About 5 papers to follow.
This is a tentative outline of the topics we will cover and will likely change as the semester goes by.
- Introduction (Jan 16)
Reading: Boyd and Vandenberghe, Chapter 1.
- Convex sets (Jan 18, 23 & 25)
Reading: Boyd and Vandenberghe, Chapter 2.
- Convex Functions (Jan 30, Feb 1 & 6)
Reading: Boyd and Vandenberghe, Chapter 3.
- Convex Optimization Problems (Feb 6, 8, 13 & 15)
Reading: Boyd and Vandenberghe, Chapter 4.
- Duality (Feb 20, 22, 27 & Mar 1)
Reading: Boyd and Vandenberghe, Chapter 5.1-5.7, 5.9.
- Approximation and Fitting (Mar 6 & 8)
Reading: Boyd and Vandenberghe, Chapter 6.
- Statistical Estimation (Mar 13 & 15)
Reading: Boyd and Vandenberghe, Chapter 7.
- Geometric Problems (Mar 20 & 22)
Reading: Boyd and Vandenberghe, Chapter 8.
- Algorithms (Apr 3, 5, 10, 12, 17, 19, 24 & 26)
Lecture Notes(Unconstrained problems)
Lecture Notes(Equality constrained problems)
Lecture Notes(Interior-point methods)
Reading: Boyd and Vandenberghe, Chapter 9, 10, 11.
- Structural Signal Recovery (May 1 & 3)
This is a preliminary breakdown that may change during the semester.
- Homework -- 40%
- Final -- 50%
- Participation -- 10%
There will be about eight to ten homework sets, due in class . Students are strongly encouraged to collaborate on homeworks, but should make sure to fully understand the problems and solutions and must write down solutions independently.
There will be a 24-hour take home final exam.
The lecture slides are adopted from Dr. Stephen Boyd's letcture notes on Convex Optimization at Standord University. Thank Dr. Boyd for his kind help and support.
Accommodations for Disability
If you qualify for accommodations because of a disability, please submit to your professor a letter from Disability Services in a timely manner (for exam accommodations provide your letter at least one week prior to the exam) so that your needs can be addressed. Disability Services determines accommodations based on documented disabilities. Contact Disability Services at 303-492-8671 or by e-mail at email@example.com.
If you have a temporary medical condition or injury, see Temporary Medical Conditions: Injuries, Surgeries, and Illnesses guidelines under Quick Links at Disability Services website and discuss your needs with your professor.
Campus policy regarding religious observances requires that faculty make every effort to deal reasonably and fairly with all students who, because of religious obligations, have conflicts with scheduled exams, assignments or required attendance. In this class, we accommodate the absences of the class and delay in homeworks and project due to religious observances, upon notifying the instructor one week ahead. See full details at http://www.colorado.edu/policies/fac_relig.html.
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The instructor reserves the right to adjust grades as he sees needed, in response to the student behavior issues.
Discrimination and Harassment
The University of Colorado Boulder (CU-Boulder) is committed to maintaining a positive learning, working, and living environment. The University of Colorado does not discriminate on the basis of race, color, national origin, sex, age, disability, creed, religion, sexual orientation, or veteran status in admission and access to, and treatment and employment in, its educational programs and activities. (Regent Law, Article 10, amended 11/8/2001). CU-Boulder will not tolerate acts of discrimination or harassment based upon Protected Classes or related retaliation against or by any employee or student. For purposes of this CU-Boulder policy, "Protected Classes" refers to race, color, national origin, sex, pregnancy, age, disability, creed, religion, sexual orientation, gender identity, gender expression, or veteran status. Individuals who believe they have been discriminated against should contact the Office of Discrimination and Harassment (ODH) at 303-492-2127 or the Office of Student Conduct (OSC) at 303-492-5550. Information about the ODH, the above referenced policies, and the campus resources available to assist individuals regarding discrimination or harassment can be obtained at http://www.colorado.edu/odh.
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