EE5121: Optimization Methods in Signal Processing & Communications (2013)

Instructor: RadhaKrishna Ganti

Slot: D

Contact Information:

  1. Phone:   2257-4467
  2. Email:  rganti [at] ee . iitm . ac . in
  3. Office: ESB 208D

We will be closely following the book “Convex Optimization” by Stephen Boyd. This book is also available online.  

Additional Textbooks:

  1. Convex Optimization by D. Bertsekas, A. Ozdaglar, and A. Nedic.
  2. 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:

  1. Introduction
  2. Foundations
  1. Basic theory
  1. Sequences, open and closed sets, continuous functions, vector spaces, inner products, norms, dual spaces.
  1. Convex sets and convex functions
  2. Separation theorems
  3. Dual Cones
  4. Conjugate functions and Fenchel’s inequality
  1. Convex optimization
  1. Linear optimization
  2. Quadratic optimization
  3. Semidefinite
  4. Duality
  1. Lagrangian
  2. KKT
  1. Subgradient Methods (optional)
  1. Applications
  1. Possible topics: Compressive sensing, Combinatorial optimization, learning theory, Convex games, Communication theory, Networks.


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

  1. Math basics
  1. Norms and Sequences   
  2. Open and closed sets
  3. Continuous functions
  4. Compact sets
  5. Basics of linear algebra
  1. Convex sets
  1. Definition and examples
  2. Caratheodeory’s theroem
  3. Application of Caratheodeory’s Theorem in Information Theory
  4. Topology of convex sets
  5. Separation theorems
  6. Faces and extreme points of a convex set: Krein-Milman theorem

Home works

  1. HW1 (Norms)
  2. HW2 (Topology)