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.

- 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.

**Location:** Eckhart Hall,
Room 133

**Times:** 2:30–3:20pm on Mon/Wed/Fri.

**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 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`

**Grade composition:** Two in-class quizzes (Feb 2 and
Mar 11) and programming assignment.

- 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.