STAT 28000. Optimization
Department of Statistics
University of Chicago
This is an introductory course on optimization that will cover the
rudiments of unconstrained and constrained optimization of a real-valued
multivariate function. The focus is on the settings where this function
is, respectively, linear, quadratic, convex, or differentiable. Time
permitting, topics such as nonsmooth, integer, vector, and dynamic
optimization may be briefly addressed. Materials will include basic
duality theory, optimality conditions, and intractability results, as well
as algorithms and applications.
- 06/01/15: Office hours 2:00–3:30pm on Fri, June 5 and Fri,
- 06/01/15: Homework 4 posted, due Monday, June 15, 5:00pm.
- 05/20/15: Quiz on Wed, May 27, 6:00–8:00pm, in Eckhart 202.
- 05/20/15: Homework 3 deadline extended to Fri, May 22, 5:00pm.
- 05/17/15: Office hours this week: Mon, 2:00–3:30pm and Wed,
- 05/12/15: Homework 3 posted, due May 21.
- 05/09/15: Make-up lecture Mon, May 11, 6:00–8:00pm, in Eckhart
- 05/09/15: Class will not meet on Tue, May 12.
- 05/05/15: Class will not meet on Thu, May 7 because
of the Bahadur lecture. Make-up date to be announced.
- 04/25/15: Homework 2 posted, due May 5.
- 04/14/15: Lecture on Thu, May 7 will end at 4:00pm because of the
- 04/11/15: Homework 1 posted, due Apr 21.
- 04/04/15: Make-up lecture Mon, Apr 6, 6:00–7:30pm in Eckhart
- 03/30/15: Check back regularly for announcements.
Hall, Room 133.
Times: Tue & Thu, 3:00–4:20pm
Office: Eckhart 122
Tel: (773) 702-4263
Office hours: Day before problem set is due, 2:00–3:30pm, Eckhart
Course Assistant: Marc
Office: Eckhart 131
Office hours: Thu, 10:00–11:00am, Eckhart 131
- Optimization of a univariate real-valued function
- Multivariate real-valued functions
- Higher-order derivatives of multivariate functions
- Multivariate Taylor expansion with remainder in mean-value form and
- Unconstrained optimization
- Newton, quasi-Newton, conjugate gradient, and steepest descent
- Constrained optimization
- Implicit function theorem and Lagrange multipliers
- KKT conditions
- Nonlinear optimization
- Convex sets and convex functions
- Convex optimization
- Newton and steepest descent methods revisited
- Linear programming
- Basic duality theory
- Brief overview of nonsmooth, integer, vector, and dynamic
Collaborations are permitted but you will need to write up your own
solutions and declare your collaborators. The problem sets are designed to
get progressively more difficult. You will get at least six days for each
You are required to implement your own programs for problems that
require some amount of simple coding (using Matlab, Mathematica, R,
Bug report on the problem sets:
Grade composition: 60% Problem Sets, 40% Quiz.
We will not use any specific textbook but will use selected material
from the following references, all of which would be accessible to
You may download all these books online from an UChicago IP address or
via ProxyIt! if you are off-campus.