E0 350: Advanced Convex Optimization

• Term: January - May 2023.

• Credits: 3:1

• Hours: Tuesday and Thursday, 10:00 - 11:30 hrs.

• Instructor: Kunal Chaudhury.  (kunal@iisc.ac.in)

• Grading: project: 30% mid-term: 30%, final: 40%. 

• Prerequisites: linear algebra, basic multivariate calculus and optimization.

• Topics: (theory) convex sets and functions, extended-real-valued convex functions, lower-semicontinuity, conjugate function, subgradient, subdifferential calculus, convex projection, supporting and separating hyperplane theorems, fixed-point iterations and convergence; proximal and averaged operators; (algorithms) gradient and subgradient descent, projected and proximal gradient descent, and ADMM.

• Lecture notes: link.

• References:  

1. First-Order Methods in Optimization by Amir Beck.

2. Lectures on Convex Optimization by Yurii Nesterov.