E0 350: Advanced Convex Optimization
Term: January - May 2022.
Credits: 3:1
Hours: Tuesday and Thursday (10:00 - 11:30 hrs).
Instructor: Kunal Chaudhury.
Prerequisites: linear algebra and real analysis.
Scope: A large part of the course will be devoted to nonsmooth convex analysis and particularly to subdifferential calculus. We will also look at the connection between monotone operator theory and convex optimization, and how this can be used to analyze many commonly used iterative algorithms for smooth and nonsmooth optimization. There will be a project component wherein the students would be asked to apply these tools to various engineering problems.
Topics: convex sets and functions, characterizations of convexity, topological properties, separation theorems, subdifferential calculus, proximal operator, iterative algorithms for smooth optimization, set-valued operators, monotone operator and fixed-point theory, operator splitting techniques for nonsmooth optimization.
References:
Convexity and Optimization in Rn by Berkovitz, 2002.
Convex Analysis by Rockafellar, 1970.
Lectures on Convex Optimization by Nesterov, 2018.
Convex Analysis and Monotone Operator Theory in Hilbert Spaces by Bauschke and Combettes, 2011.
Primer on Monotone Operator Methods by Ryu and Boyd, 2016.