E0 330: Convex Optimization and Applications


Announcements:

  1. Exam: 22nd April, 2-5 pm, B 308.

  2. Final lecture: 7th April.

  3. Second mid-term exam: 27th March, 2-4 pm, B 308.

  4. First mid-term exam: 20th February, 2-4 pm, B 308.

  5. First meeting for CVO: 5th January 2016, 10 am, B 308.

Course Details

  • Term: January - April 2016.

  • Credits: 3:1

  • Hours: Tuesday and Thursday (10:00 - 11:30 AM).

  • Instructor: Kunal N. Chaudhury (kunal@ee.iisc.ernet.in).

  • Venue: B 308.

  • Course Description: The focus of the course will be on various algorithms for solving generic and structured convex optimization problems, and their analysis. In the process, the students will be introduced to relevant topics in convex analysis and duality. Various applications of convex optimization in inverse problems, signal processing, image reconstruction, statistics, and machine learning will be discussed.

  • Prerequisites: A course in linear algebra is mandatory. Familiarity with multivariate calculus and real analysis will be helpful. Prior to this course, I strongly suggest taking Computational Methods of Optimization or Linear and Non-Linear Optimization, both offered in August-December.

  • Topics (# lectures):

  1. Introduction to Convex Optimization (3).

  2. Applications (3).

  3. Background Topics in Real Analysis (3).

  4. Fundamentals of Convex Analysis (6).

  5. Analysis of (Accelerated) Gradient and Subgradient Methods (5).

  6. Lagrange Duality (6).

  7. More Applications (2).

  • Course structure: About 28 lectures, 2 mid-term exams, 4 assignments (math problems and coding), and a final exam.

  • Grading: Assignments: 20%, Mid-term exams: 30%, Final exam: 50%.

  • References:

  1. Bretsekas, Convex Optimization Algorithms.

  2. Nesterov, Introductory Lectures on Convex Programming.

  3. Boyd and Vandenberghe, Convex Optimization.