STAT 31015. Mathematical Computation IIA — Convex Optimization

Department of Statistics
University of Chicago
Winter 2015

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.

Announcements

• 03/07/15: Quiz 2 next Wed (Mar 11), 2:30–3:20pm.

• 02/25/15: Programming assignment posted.

• 01/30/15: Quiz 1 next Mon (Feb 2), 2:30–3:20pm.

• 01/23/15: Stephen Boyd's lecture next Mon, Jan 26, 11:00am–12:00n in TTIC Room 526.

• 01/12/15: Make-up lectures 6:30–8:00pm in E133 tonight (Jan 12) and tomorrow night (Jan 13).

• 01/05/15: Check back regularly for announcements.

Lectures

Location: Eckhart Hall, Room 133

Times: 2:30–3:20pm on Mon/Wed/Fri.

Course staff

Instructor: Lek-Heng Lim
Office: Eckhart 122
lekheng(at)galton.uchicago.edu
Tel: (773) 702-4263
Office hours: Fri 3:30–5:00 PM

Course Assistant: Marc Goessling
Office: Eckhart 131
goessling(at)galton.uchicago.edu
Office hours: Tue 4:00–5:00 PM

Problem Sets

• Problem Set 4: Excercises 4.33, 4.34, 4.39, 4.41, 4.48, 5.3, 5.5, 5.7, 5.10, 5.13, 5.21, 5.27, 5.28, 5.30 in the book (posted: Mar 2)

• Programming Assignment: Check your email for the link to the required files (posted: Feb 25)

• Problem Set 3: Excercises 4.3, 4.5, 4.8, 4.9, 4.12, 4.13, 4.18, 4.21, 4.22, 4.23, 4.24, 4.26, 4.28, 4.29 in the book (posted: Feb 10)

• Problem Set 2: Excercises 3.4, 3.13, 3.20, 3.24, 3.25, 3.32, 3.36, 3.37, 3.39, 3.49, 3.52, 3.54, 3.55, 3.56 in the book (posted: Jan 23)

• Problem Set 1: Excercises 2.2, 2.10, 2.11, 2.13, 2.15, 2.16, 2.19, 2.20, 2.23, 2.26, 2.31, 2.32, 2.35, 2.36 in the book (posted: Jan 13)

Bug report on the problem sets: lekheng(at)galton.uchicago.edu

• S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.

• J. Lasserre, Moments, Positive Polynomials and their Applications, Imperial College Press, 2010.

• J. Nocedal and S. Wright, Numerical Optimization, 2nd Ed, Springer, 2006.