This course covers the fundamentals of convex optimization. Topics will include basic convex geometry and convex analysis, KKT condition, Fenchel and Lagrange duality theory; six standard convex optimization problems and their properties and applications: linear programming, geometric programming, second-order cone programming, semidefinite programming, linearly and quadratically constrained quadratic programming. In the last part of the course we will examine the generalized moment problem — a powerful technique that allows one to encode a wide variety of problems (in probability, statistics, control theory, financial mathematics, signal processing, etc) and solve them or their relaxations as convex optimization problems.
Location: Eckhart Hall, Room 133
Times: 2:30–3:20pm on Mon/Wed/Fri.
Office: Eckhart 122
Tel: (773) 702-4263
Office hours: Fri 3:30–5:00 PM
Course Assistant: Marc
Office: Eckhart 131
Office hours: Tue 4:00–5:00 PM
Bug report on the problem sets: lekheng(at)galton.uchicago.edu
Grade composition: Two in-class quizzes (Feb 2 and Mar 11) and programming assignment.