Ph.D. Level Courses

Convex Optimization for Signal Processing and Communications

Objective

The main goal of this course is to introduce the basic theory of convex optimization. Additionally, some applications will be highlighted with focus on research problems in the area of signal processing and communications.

Instructor

Dr. <Unknown username: karipidis>, ISY/Communication Systems.

Registration

The course is open to students enrolled in a Ph.D. program at Linkoping University. If you have interest to participate, please register by sending an email to karipidis@isy.liu.se.

Prerequisites

Good knowledge of linear algebra. General mathematical maturity. Exposure to numerical optimization helpful but not required.

Outline

The content is mainly based on the course material developed by Stephen Boyd (Stanford University) and Lieven Vandenberghe (UCLA).

Literature

The main coursebook is Convex Optimization, S. Boyd and L. Vandenberghe.

Additional literature:

• Convex Optimization in Signal Processing and Communications, D. Palomar and Y. Eldar
• Convex Optimization for Signal Processing, IEEE Signal Processing Magazine, vol. 27, no. 3, May 2010
• Introductory Lectures on Convex Optimization: A Basic Course, Y. Nesterov
• Convex Optimization Theory, D. Bertsekas

Schedule

The lectures and homework sessions are scheduled on Mondays at 13:15 and Wednesdays at 9:15. They are held in Signalen (house B, entrance 27, ground floor) unless noted otherwise. The schedule will be fine tuned, at least one week ahead, in coordination with the participating students.

• Mon, 2013.01.21, 13:15 - Ch. 1: Introduction
• Mon, 2013.01.28, 13:15 - Ch. 2: Convex sets
• Mon, 2013.02.04, 13:15 - Ch. 3: Convex functions
• Wed, 2013.02.06, 9:15 - Ch. 3: Convex functions
• Mon, 2013.02.11, 13:15 - HWK 1: Convex sets
• Mon, 2013.02.18, 13:15 - HWK 2: Convex functions
• Wed, 2013.02.20, 9:15 - Ch. 4: Convex optimization problems
• Mon, 2013.02.25, 13:15 (Algoritmen)<\b> - Ch. 4: Convex optimization problems
• Wed, 2013.03.06, 9:15 (Algoritmen)<\b> - Ch. 5: Duality
• Mon, 2013.03.18, 13:15 - HWK 3: Convex optimization problems
• Wed, 2013.03.22, 15:30 - Ch. 5: Duality
• Mon, 2013.03.25, 13:15 - HWK 3: Convex optimization problems
• Wed, 2013.04.03, 9:15 - Ch. 9: Unconstrained minimization
• Wed, 2013.04.10, 9:15 - HWK 4: Duality
• Mon, 2013.04.15, 13:15 - HWK 4: Duality
• Wed, 2013.04.17, 9:15 - Ch. 10: Equality constrained minimization
• Thu, 2013.05.02, 13:15 - Ch. 11: Interior-point methods
• Mon, 2013.05.13, 13:15 - Ch. 11: Interior-point methods

  Homeworks

  The problems are from the coursebook Convex Optimization, S. Boyd and L. Vandenberghe. The deadlines are strict. You are requested to hand in the solutions at the beginning of the homework session and be prepared to present any of the solutions during the session.
  • HWK 1, 2013.02.11:
    2.5, 2.7, 2.11, 2.12, 2.15, 2.19, 2.28, 2.29, 2.33
  • HWK 2, 2013.02.18:
    3.5, 3.8, 3.18, 3.21(b), 3.22(b,c), 3.23, 3.26, 3.32, 3.33, 3.42, 3.54, 3.55
  • HWK 3, 2013.03.18,25:
    4.1, 4.3, 4.6, 4.8(a-d), 4.11, 4.12, 4.13, 4.15, 4.24, 4.26, 4.33, 4.35, 4.37, 4.40, 4.42, 4.43(c), 4.45, 4.57, 4.62
  • HWK 4, 2013.04.10,15:
    5.1, 5.7, 5.12, 5.13, 5.39, 5.21, 5.22, 5.26, 5.27, 5.29, 5.31, 5.32
  • HWK 5, 2013.05.20:
    11.23

  Examination

  • There will be a final take-home exam.
  • The evaluation will be based upon the submitted homework solutions, their presentations, and final exam.
  • The course yields 8 credits.
  
  

  Page responsible: Lefteris Karipidis
  Last updated: 2016 02 23   19:04