EE5121: Optimization Methods in Signal Processing & Communications (2013)
Instructor: RadhaKrishna Ganti
Slot: D
Contact Information:
- Phone: 2257-4467
- Email: rganti [at] ee . iitm . ac . in
- Office: ESB 208D
We will be closely following the book “Convex Optimization” by Stephen Boyd. This book is also available online.
Additional Textbooks:
- Convex Optimization by D. Bertsekas, A. Ozdaglar, and A. Nedic.
- A Course in Convexity by A. Barvinok
I will also use additional references whenever necessary.
Prerequisites: Knowledge of linear algebra and real analysis is desirable but not necessary. If you have any questions regarding the prerequisites and your background, please drop an email.
Course Contents:
- Introduction
- Foundations
- Basic theory
- Sequences, open and closed sets, continuous functions, vector spaces, inner products, norms, dual spaces.
- Convex sets and convex functions
- Separation theorems
- Dual Cones
- Conjugate functions and Fenchel’s inequality
- Convex optimization
- Linear optimization
- Quadratic optimization
- Semidefinite
- Duality
- Lagrangian
- KKT
- Subgradient Methods (optional)
- Applications
- Possible topics: Compressive sensing, Combinatorial optimization, learning theory, Convex games, Communication theory, Networks.
Grading:
Homework: 30%
Quiz : 20%
Project : 20%
Finals : 30%
Homework: There will be a weekly homework that will be graded. Homework constitutes about 30% of the grade and will be taken very seriously.
Office hours: Once the course gets started, I will conduct regular office hours.
Lecture notes: I will post the lecture notes at the following blog
- Math basics
- Norms and Sequences
- Open and closed sets
- Continuous functions
- Compact sets
- Basics of linear algebra
- Convex sets
- Definition and examples
- Caratheodeory’s theroem
- Application of Caratheodeory’s Theorem in Information Theory
- Topology of convex sets
- Separation theorems
- Faces and extreme points of a convex set: Krein-Milman theorem
Home works
- HW1 (Norms)
- HW2 (Topology)