Convex Analysis Spring 2005
M. C. Pinar
Monday 15:30-17:00, Wednesday 14:30-17:00
Reference Materials and Online Resources:
- Convex Optimization, S.
and L. Vandenberghe, Cambridge Univ. Press, 2004.
The material listed above
is for students' reference. The course will be based on the
textbook. This is the second time
- 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.
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
to Convex and Quasi-Convex Analysis, by J.B.G. Frenk
and G. Kassay, 2001.
in Convex Optimization and Engineering , by A. Ben-Tal and A.
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.
- Convex sets
- Convex functions
- Linear and
quadratic programming problems
- Geometric and
- Duality and
and data fitting problems
Exercises 2.10, 2.11, 2.17 and 2.19, due 17.2.2005, Thursday.
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.
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
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
- 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.
| Term paper: