This course covers the fundamentals of convex optimization. We will talk about mathematical fundamentals, modeling (how to set up optimization problems for different applications), and algorithms.
Instructor: Justin Romberg
Course Notes
Notes 1, introduction and example (see also: intro slides)
I. Convexity
Notes 2, convex sets
Notes 3, convex functions
II. Unconstrained Optimization
Notes 4, optimality conditions iterative descent methods, line search
Notes 5, gradient descent
Notes 6, accelerated first-order methods
Notes 7, Newton’s method and quasi-Newton methods
Notes 8, nonsmooth optimization, subgradients and subdifferentials
Notes 9, proximal algorithms
III. Constrained Optimization
Notes 10, geometric conditions for solving constrained problems
Notes 11, KKT conditions
Notes 12, Lagrange duality
Notes 13, Fenchel duality
Homework
Homework 1, due Thursday January 16
Homework 2, due Thursday January 23. You will need the file hw02_prob06.py.
Homework 3, due Thursday January 30.
Homework 4, due Friday February 14. You will need the file hw04p6.py
Homework 5, due Friday February 21. You will need the file hw05p6.mat
Homework 6, due Friday February 28.
Homework 7, due Friday March 14.