Instructor
Justin Romberg
Email: jrom@ece.gatech.edu
Office: Centergy 5227
Phone: 404-894-3930
Description
This course covers the fundamentals of convex optimization. We will discuss mathematical fundamentals, modeling (how to set up optimization algorithms for different applications), and algorithms.
Outline
I. Introduction to optimization, example problems
II. Convexity
a) convex sets
b) closest point problem and its dual
c) convex functions
d) Fenchel duality
III. Unconstrained optimization
a) basic theory
b) gradient descent
c) accelerated first-order methods
d) Newton’s method
e) quasi-Newton methods
IV. Constrained optimization
a) geometric optimality conditions
b) KKT conditions
c) Lagrange duality with examples
d) interior point methods
e) ADMM
V. Modeling
a) applications in engineering, statistics, and machine learning
b) convex relaxations
VI. Non-smooth optimization
a) subgradients and basic theory
b) subgradient method
c) proximal methods
d) proximal gradient (forward-backward splitting)
