Introduction to Optimization |
CO 250
Winter 2019 |
Lecture times and locations:
Section |
Instructors |
Rooms |
Days & Times |
1 |
Henry Wolkowicz |
Tu, Th 10:00AM - 11:20AM | |
2 |
Peter Nelson |
Mo, We, Fr 9:30AM - 10:20AM |
Tutorials and
office hours:
Rooms |
Days & Times |
|
Office hours: Nelson |
MC 5128 |
TBA |
Office hours: Wolkowicz |
MC 6312 |
TBA |
Office hours (TAs) |
TBA |
TBA |
Office hours (TAs) |
TBA |
TBA |
Office hours (TAs) | TBA |
TBA |
You can attend either of the instructor's office hours.
Students are strongly encouraged to attend office hours.
We are here to help, but we can only help you if you take advantage of the resources available to you.
Contact
information:
Name |
email contact |
Responsibility |
Office & Contact |
Henry Wolkowicz |
henry.wolkowicz@uwaterloo.ca |
Instructor Section 1 |
MC 6312, x35589 |
Peter Nelson |
apnelson@uwaterloo.ca |
Instructor Section 2 |
MC 5128, x37300 |
Important: make sure to indicate in the
subject line the course number and the section number (example
CO250-001), failure to do this may result in delayed answers.
For questions pertaining to the current assignment please use the piazza forum which is setup on D2L.
Website:
We will be using D2L as
our course website. Log on using your username and password
(same as your UW email account).
The solutions will be posted there. Various announcements such
as the dates of exams or corrections to assignments will be
posted there.
It
is the responsibility of the students to check the web page
regularly.
Discussion
board:
Overview:
Suppose that the owner of a factory wants to maximize its production for the next 30 days. There is a limit on the resources available. Resources may include, raw materials, labor, machine capacities, etc. This is an example of an optimization problem. The function that we are trying to maximize is the objective function, and the conditions imposed by the available resources are the constraints of the problem. Optimization problems are classified according to the type of objective function and the type of constraints. The simplest models are Linear Programs where both the constraints and the objective functions are linear. Even though this may appear at a first glance to be overly restrictive, linear programming algorithms are used widely across most branches of industry. Indeed, a recent survey of Fortune 500 companies shows that 85% of all respondents use such algorithms in their operations. It is not hard however, to imagine applications for which fractional variable values are not desirable. For instance a variable may indicate the number of employees to hire, or a variable may be restricted to values 0 or 1 to indicate one of two possible options (e.g., build a factory in Waterloo or don't). In these cases we would like to add the condition that some variables in our linear program take integer values only. These models are known as Integer Programs. Finally, in certain instances, such as portfolio optimization (in financial mathematics), the natural way of formulating the optimization problem may require the use of non-linear constraints, or a non-linear objective function. |
Geometric Representation of the Simplex
Algorithm |
In the first two weeks of the course, we will illustrate
these various models with examples that arise from real
problems. In the remainder of the course we address the problem
of how to solve the aforementioned problems. The Simplex algorithm to solve
Linear Programs will be discussed in some detail and
general-purpose Integer Programming techniques such as Branch-and-Bound and Cutting Planes will also be
described. These algorithms while guaranteed to terminate, may
in the worst case (and often do in practice) take a
prohibitively long time. No fast general algorithm is known for
integer programs (and none is believed to exist), however, there
are efficient algorithms for many important special cases such
as the Shortest Path problem. An indispensable
tool for the design of such fast algorithms is the Theory of Duality, which
will be a main focus of this course. The other important idea is
the notion of relaxations.
All of these ideas come together at the conclusion of the course
when we discuss non-linear convex optimization problems
Schedule:
This is a tentative
schedule,
Week |
Starts on |
Topic |
Book sections |
HW out (Friday) |
HW
due (Friday) |
Comments |
1 |
January 7th |
Formulations |
1.1 |
1 |
- |
no office hours |
2 |
January
14th |
Formulations |
1.2-1.4 |
2 |
1 |
|
3 | January
21th |
Formulations/Outcomes | 1.4, 1.6 |
3 |
2 |
|
4 | January
28th |
SEF,
Basis |
2.1, 2.2 |
4 |
3 |
|
5 | February
4th |
Simplex |
2.3-2.5 |
5 |
4 |
Midterm 1 (date TBA) |
6 |
February
11th |
Simplex,
Geometry |
2.6 |
6 |
5 |
|
7 | February 18th | - |
- |
READING WEEK |
||
8 | February
25th |
Shortest path/duality |
2.8,3.1 |
- |
- |
|
9 |
March 4th |
Shortest path/duality |
3.1 |
7 |
6 | |
10 |
March
11th |
Duality | 4.1-4.3 |
8 | 7 | |
11 |
March 18th | IP | 6.1-6.2 |
9 |
8 |
Midterm 2 (date TBA) |
12 | March 25th | NLP | 7.1, 7.2 |
10 | 9 |
|
13 | April
1st |
NLP, recap | 7.3-7.5 |
- |
10 |
Objectives:
Students will be expected to master the following tasks
and concepts:
Note, regarding
algorithms, while it is necessary to know how to carry simple
computations by hand, it is not sufficient.
We will expect students to have a good understanding of why
algorithms return correct answers and how they are derived.
Class attendance:
It has
been the instructors’ experience that students missing class
regularly tend to get grades much below average.
You are unlikely to pass the course if you regularly fail to attend class. |
There will
be 10 assignments.
No credit will be given for
assignments but all assignments will be graded (we will use
Crowdmark).
The
decision not
to assign credit is
based the following factors:
The midterms and the final
exam will be heavily based on the material covered in the
assignments. You are unlikely to pass the course if you do not spend substantial time on every single assignment. |
There will be two in-class
midterms on
the following dates:
In
case you have a conflict with that date and time, please
contact your instructor as soon as possible.
If you have any complaints about the
marking of the midterm, then you should first check your
solutions against the posted solutions.
After that if you see any marking error, then you should
return the exam paper to your instructor within two
weeks.
Computing your final grade:
Midterm 1 |
25% |
Midterm 2 |
25% |
Final |
45% |
Piazza participation |
5% |
INC
grade:
A grade of INC (incomplete) will be only awarded to students who cannot write the final exam for reasons acceptable to the instructor, such as a medical certificate by a recognized medical professional. In addition such students need to be in good standing prior to the final exam. To be in good standing a student must have written and passed both midterm exams.
4. Academic
Integrity/Accessibility services:
In order to maintain a culture of academic integrity, members of the University of Waterloo community are expected to promote honesty, trust, fairness, respect and responsibility.
Grievance: A student who
believes that a decision affecting some aspect of
his/her university life has been unfair or unreasonable
may have grounds for initiating a grievance.
Read Policy #70, Student Petitions and Grievances, Section 4. http://www.adm.uwaterloo.ca/infosec/Policies/policy70.htm
Discipline: A student is
expected to know what constitutes academic integrity, to
avoid committing academic offenses, and to take
responsibility for his/her actions. A student who is
unsure whether an action constitutes an offense, or who
needs help in learning how to avoid offenses (e.g.,
plagiarism, cheating) or about “rules” for group
work/collaboration should seek guidance from the course
professor, academic advisor, or the Undergraduate
Associate Dean.
For information on categories of offenses and types of penalties, students should refer to Policy #71, Student Discipline, http://www.adm.uwaterloo.ca/infosec/Policies/policy71.htm
Appeals: Concerning a decision
made under Policy #70 (Student Petitions and Grievances)
(other than petitions) or Policy #71 (Student
Discipline) a student may appeal the finding, the
penalty, or both.
A student who believes he/she has a
ground for an appeal should refer to Policy #72 (Student
Appeals) http://www.adm.uwaterloo.ca/infosec/Policies/policy72.htm
Note for students with disabilities: AccessAbility Services, located in Needles Hall, Room 1401, collaborates with all academic departments to arrange appropriate accommodations for students with disabilities without compromising the academic integrity of the curriculum. If you require academic accommodations to lessen the impact of your disability, please register with AccessAbility Services at the beginning of each academic term.