STAT 28000/CAAM 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.
- 05/30/19: Lecture Notes 16 posted.
- 05/28/19: Office hours Thu, May 30, 2:00–3:00pm
- 05/24/19: Lecture Notes 15 posted.
- 05/21/19: No lecture on Tue, May 28, but TA will be in Eckhart 133
from 3:30–3:45pm to pick up Homework 4.
- 05/21/19: Lecture Notes 14 posted.
- 05/18/19: Office hours Fri, May 24, 2:00–4:00pm
- 05/16/19: Lecture Notes 13 posted.
- 05/14/19: Homework 4 and Lecture Notes 12 posted.
- 05/09/19: Lecture Notes 11 posted.
- 05/08/19: Office hours Thu, May 9, 2:00–3:00pm and Mon,
May 13, 2:00–4:00pm.
- 05/07/19: Lecture Notes 10 posted.
- 05/02/19: Lecture Notes 9 posted.
- 04/30/19: Homework 3 posted.
- 04/30/19: Lecture Notes 7 and 8 posted.
- 04/26/19: Office hours Mon, Apr 29, 1:00–2:30pm.
- 04/20/19: Office hours Tue, Apr 23, 2:00–3:00pm.
- 04/19/19: Lecture Notes 5 and 6 posted.
- 04/18/19: Homework 2 posted.
- 04/17/19: Lecture Notes 4 posted. Video of
tonight's make-up lecture available (same password).
- 04/16/19: Office hours Wed, Apr 17, 3:00–5:00pm; reminder:
make-up lecture 6:00–8:00pm.
- 04/11/19: Lecture Notes 3 posted. Video of
yesterday's make-up lecture available.
- 04/10/19: Lecture Notes 2 posted.
- 04/09/19: Make-up lectures 6:00–8:00pm on Weds, Apr 10 and
17 in Eckhart 133.
- 04/09/19: Homework 1 posted.
- 04/09/19: Lecture Notes 0 and 1 posted.
- 03/29/19: No lectures in the first week, i.e., class
will not meet Apr 2 and 4.
- 03/29/19: Check back regularly for announcements.
Hall, Room 133.
Times: Tue & Thu, 3:30–4:50pm
Office: Jones 122C
Tel: (773) 702-4263
Office hours: Two hours in weeks when a problem set is due, one hour in
other weeks. Venue: Jones 122C. Times would be announced by email.
Course Assistant I: Zhipeng
Office hours: 5:30–7:00pm Mon, Jones 226
Course Assistant II: Zhisheng
Office hours: 10:00–11:20am, Tue, Searle 206
Course Assistant III: Lijia
Office hours: 10:30–11:50am, Wed, Jones 304
- 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
- Methods of penalty function, augmented Lagrangian, and barrier
- 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:
Grades and quizzes
Grade composition: 60% Problem Sets, 40% Quizzes.
Quizzes: Quiz I on Thu, Apr 25, 3:30–4:50pm,
Eckhart 133. Quiz II on Tue, Jun 4, 3:30–4:50pm,
Closed book, closed notes, no cheat sheet.
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.