Convex Optimization, Spring 2017

Justin Romberg
Office: Centergy 5227
Phone: 404-894-3930

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.

Download the syllabus (pdf)


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

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)