This course covers the fundamentals of convex optimization. Students are expected to have a solid grounding in multivariate calculus and linear algebra, and will be expected to complete several programming exercises (using CVX, SeDuMi, SDPT3, or SDPA) during the course.
General topics covered will include basic convex geometry and convex analysis, KKT condition, self-concordance, Fenchel and Lagrange duality theory. The main focus of the course will be the various types of convex optimization problems and their applications to science, medicine, and engineering problems. These include 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 singularly powerful technique that allows one to encode all kinds 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 117
Times: 3:00–4:20pm on Tue/Thu.
Office: Eckhart 122
Tel: (773) 702-4263
Office hours: Weds 1:30-3:30 PM
Course Assistant: Lian
Office: Eckhart 131
Office hours: Tues 12:00-1:00 PM
Problem set will be assigned biweekly. Collaborations are permitted but you will need to write up your own solutions.
Bug report on the problem sets or the solutions: lekheng(at)galton.uchicago.edu
Grade composition: No in-class examination. Grade based entirely on five take-home problem sets.