EEOR E4650: Convex Optimization

Instructor: Javad Lavaei
Time: Monday, 10:10 am-12:40 pm
Location: MUDD 834
Office Hours: Mondays, 2-4 pm
TA: Ramtin Madani, rm3122@columbia.edu
Grading Policy:

• 30% homework

• 25% midterm exam

• 45% course project

Description

Syllabus:

• Convex sets and functions

• Convex optimization

• Duality

• Numerical algorithms

• Decomposition and distributed algorithms

• Linear matrix inequality

• Sum-of-squares technique

• Application in communications: TCP and congestion control

• Application in control: stability, robust control and optimal control

• Application in signal processing: compressed sensing

• Application in circuits: circuit design

• Application in power systems: optimal power flow

References:

• Main textbook: “Convex Optimization” by Stephen Boyd and Lieven Vandenberghe (available online at http:www.stanford.edu boydcvxbook/)

• Research papers

Lecture Notes

• Week 1: Overview and introduction (Chapter 1)

• Week 2: Convex sets and functions (Chapters 2-3)

• Week 3: Convex optimization (Chapter 4)

• Week 4: Conic optimization & examples (Chapter 4)

• Week 5: Duality theory (Chapter 5)

• Week 6: KKT conditions and midterm review (Chapter 5)

• Week 7: Numerical algorithms for unconstrained optimization (Chapter 9)

• Week 8: Primal-dual algorithm, distributed computation, optimization for communication networks (Chapters 10-11)

• Week 9: LMI formulation of stability and optimal control (LQR and LQG)

• Week 10: Optimization for power systems

• Week 11: Compressed sensing, summary of the course (materials: 1 and 2)

Homework

• Homework 1

• Homework 2

• Homework 3

• Homework 4

• Homework 5