### 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)