University of Chicago

Winter 2011

This course covers the fundamentals of continuous optimization, linear programming, and convex optimization. Students are expected to have a solid grounding in multivariate calculus and linear algebra, and will be expected to complete several substantial programming projects (using MATLAB) during the course.

Topics covered will include the simplex algorithm, duality, line search and trust region methods for unconstrained optimization, nonlinear equations and nonlinear least-squares problems, interior-point and augmented Lagrangian methods for constrained optimization, and semi-definite programming.

This web page is for the second part of the course. The web page for the first part is here. The main focus of this part will be the following three convex optimization techniques: geometric programming, second-order cone programming, semidefinite programming.

- 03/01/11: Special arrangement for office hours this week. 3:30–4 today and 2:30–4 tomorrow.

- 02/06/11: Check back regularly for announcements.

**Location:** Harper Memorial,
Room 102

**Times:** 1:30–2:50PM on Tue/Thu.

**Instructors:** Mihai
Anitescu (Part I) and Lek-Heng
Lim (Part II)

Office: Eckhart
122

`lekheng(at)galton.uchicago.edu`

Tel: (773) 702-4263

**Office hours:** Wed 1:30-2:30 PM, Thu 3:00–4:00 PM

**Course Assistant:** Han Han

Office: Ryerson N375

`han(at)galton.uchicago.edu`

**Office hours:** TBA

Problem set will be assigned weekly and will be due the following week. Collaborations are permitted but you will need to write up your own solutions.

- Problem Set 8: Do Problems 5.5, 5.6, 5.7, 5.27 (posted: Mar 11; due: Mar 18)

- Problem Set 7: Do Problems 3.36(a)–(d), 3.38, 3.39, 5.1, 5.3 (posted: Mar 4; due: Mar 10)

- Problem Set 6: Do Problems 2.15, 2.16, 2.23, 3.4, 3.8, 3.24 (posted: Feb 25; due: Mar 3)

- Problem Set 5: Do Problems 4.26, 4.33, 4.39, 4.42 (posted: Feb 17; due: Feb 24)

**Bug report** on the problem sets or the solutions:
`lekheng(at)galton.uchicago.edu`

**Grade composition:** No in-class examination. Grade based entirely
on eight take-home problem sets.

- S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge, 2004.

- S. Boyd, S.-J. Kim, L. Vandenberghe, A. Hassibi,
"A tutorial on geometric programming,"
*Optim. Eng.*,**8**(2007), no. 1, pp. 67–127.

- M. Lobo, L. Vandenberghe, S. Boyd, H. Lebret,
"Applications of second-order cone
programming,"
*Linear Algebra Appl.*,**284**(1998), pp. 193–228.

- L. Vandenberghe, S. Boyd,
"Semidefinite programming,"
*SIAM Rev.*,**38**(1996), no. 1, pp. 49–95.

- J. Renegar, A mathematical view of interior-point methods in convex optimization, SIAM, 2001.