Laboratory for Control, Optimization, and Power 
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ELEN 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  (6-8 sets),  25% midterm exam, 45% course project

Homework: Set 1 (due on Sep 26),  Set 2 (due on Oct 10), Set 3 (due on Oct 28), Set 4 (due on Nov 25), Set 5 (due on Dec 10)

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)

 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/~boyd/cvxbook/)

     Research papers