Instructor: M. C. Pinar

Room: 305

Office Hours: Monday 15:30-17:00, Wednesday 14:30-17:00

Textbook:

**Convex Optimization**, S. Boyd and L. Vandenberghe, Cambridge Univ. Press, 2004.

**Convex Analysis**by R.T. Rockafellar, Princeton University Press, 1970.**Fundamentals of Convex Analysis**, by J.B. Hirriart-Urruty and C. Lemarechal, Springer-Verlag, 2001.**Convex Analysis: An Introductory Text**, by Jan van Tiel, John Wiley and Sons, 1984.- Convex
Analysis and Optimization: Lecture Notes by A. Nemirovski, Technion.

- Chapter 1 of
**Convex Bodies: The Brunn-Minkowski Theory,**by R. Schneider, Cambridge Univ. Press, 1993 - Introduction to Convex and Quasi-Convex Analysis, by J.B.G. Frenk and G. Kassay, 2001.
- Lectures in Convex Optimization and Engineering , by A. Ben-Tal and A. Nemirovski, 1998.

the course will be offered. It will be entirely different from the previous offering. The previous (2003) edition of the course covered a classical and highly theoretical convex analysis material. The current edition will be geared towards practical recognition, formulation and solution of convex optimization problems. The students will be required to familiarize with MATLAB and to solve numerical problems.

Course Contents:

- Convex sets

- Convex functions

- Convex
optimization problems

- Linear and
quadratic programming problems

- Geometric and
Semidefinite Programming

- Duality and
optimality conditions

- Geometric and data fitting problems
- Engineering design applications

Homeworks

1. HW1:
Exercises 2.10, 2.11, 2.17 and 2.19, due 17.2.2005, Thursday.

2. HW2:
Exercises 2.20 (you do not have to prove the hint), 2.21, 2.24, 2.33
and 2.35, due 24.2.2005, Thursday.

3. HW3:
Exercises 3.7, 3.11, 3.13, 3.16 a,c,e only for convexity and concavity,
due 3.3.2005, Thursday.

4. HW4: Exercises 3.18 (a), 3.27, 3.36 (a)
and (f) only, 3.37, 3.42 due 10.3.2005, Thursday.

5. HW5: Exercises 4.7, 4.13, 4.14, 4.16,
4.20 due 17.3.2005, Thursday.

6. HW6: Exercises 4.28, 4.57, 4.58, 4.59 due
24.3.2005, Thursday.

7. HW7: Exercises 5.6, 5.13, 5.17, 5.20 and
5.28(solve the LP problem in the question using the software system
SEDUMI with the YALMIP interface.) due 8.4.2005, Friday.

8. HW8: Exercises 6.4, 6.5 and
6.8, due 2.5.2005, Monday.

9. HW9: Exercises 7.2,7.3,7.4, and the
problem assigned in class, due 10.5.2005, Tuesday.

10. HW10: Exercises 8.2 (a) and (c), 8.3 (b), 8.6,
8.8 (a), 8.15
due 20.5.2005, Friday (hand-in the hws to Ms. A. Altin).

Policy on Homework

- The lowest HW grade will be dropped.

- Your success in the course depends greatly on doing the homework
exercises on your own.

- I will assign the hw questions, usually on Thursdays.
- Late hws will not be accepted.
- There will be a term project the details of which will be decided
after the semester begins

- Cheating in homework and exams has serious consequences. Therefore, all work submitted should reflect your own effort.

Grading

Homeworks

60 %

Term paper: 40 %