EE 698W: Convex Optimization in SP/COM

  1. Instructors: Ketan Rajawat
  2. Units: 3-0-0-4
  3. Prerequisites: EE605+EE621 OR Instructor Consent 
  4. Objective: Convex optimization has recently been applied to a wide variety of problems in EE, especially in signal processing, communications, and networks. The aim of this course is to train the students in application and analysis of convex optimization problems in signal processing and wireless communications. At the end of this course, the students are expected to:
    1. Know about the applications of convex optimization in signal processing, wireless communications, and networking research.
    2. Be able to recognize convex optimization problems arising in these areas.
    3. Be able to recognize ‘hidden’ convexity in many seemingly non-convex problems; formulate them as convex problems. 
    4. Be able to develop low-complexity, approximate solutions for difficult non-convex problems.
  5. References:
    1. Stephen Boyd and Lieven Vandenberghe, Convex Optimization, Cambridge University Press. [Online].
    2. IEEE Signal Processing Magazine- Special Issue on Advances in Convex Optimization, Vol. 27, No. 3, May 2010.
    3. Dimitri P. Bertsekas, Convex Analysis and Optimization, Athena-Scientific, 2003.
  6. Format (tentative)
    1. Major quiz (15) scheduled on 29 Jan
    2. Mid-sem exam (20) scheduled on Feb 22 in L16
    3. End-sem exam (30) scheduled on April 25 at 4-7pm in L16 
    4. 2 Assignments (5x2)  handed out on 15 Jan (due 22 Jan) and 3 March (due 12 March) 
    5. 1 Computer Assignment (5x1) handed out on 30 Jan (due 26 Feb) 
    6. 1 Term paper (20) handed out on 26 March (due 18 April)
  7. Time and place: MW 2-3:30pm, L12
  8. This course will cover (approximately):
    1. Background on linear algebra
    2. Convex sets, functions, and problems
    3. Examples of convex problems: LP, QCQP, SOCP
    4. Duality, KKT conditions
    5. Geometric programming and applications
    6. Linear and quadratic classification
    7. Network optimization
    8. Sparse regression, Lasso, ridge regression and applications in image processing
    9. Robust least squares and applications in signal processing
    10. Support vector machines and applications in machine learning
    11. Semidefinite programming and applications in experiment design
    12. Semidefinite relaxation and applications in MIMO detection, integer programming
    13. Low rank matrix completion and applications in recommendor systems
    14. Multidimensional scaling and applications in sensor localization
    15. Numerical linear algebra, basics of interior point methods
  9. Course material
    1. Proof that operator norm is a norm
    2. Assignment 1, Solutions to assignment 1
    3. Assignment 2, due 23 Jan
    4. Computer Assignment 1: 5.3, 5.4, 5.6, 5.7, 5.13 from Boyd's additional exercises due 26 Feb