Introduction to Optimization



CO 250

Winter 2019


  1. Basic information:

  2. Course description:

  3. Grades and expectations:

  4. Academic Integrity/Students with Disabilities:


1. Basic information:

Lecture times and locations:

Section

Instructors

Rooms

Days & Times

1

Henry Wolkowicz

MC   4021

Tu, Th 10:00AM - 11:20AM

2

Peter Nelson

RCH   103

Mo, We, Fr 9:30AM - 10:20AM


Tutorials and office hours:

Office hours will run from January 14th to April 5th.
There will be no office hours during the study break (February 19th to February 22nd).

 

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

The office hours will be the appropriate forum for all questions pertaining to the course material and to assignments.

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:

https://learn.uwaterloo.ca/

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:

Text book:

2. Course description:

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
Picture courtesy Rex K. Kincaid


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


3. Grades and expectations:

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.


Assignments:

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:

  1. It has been the experience of this (and other instructors) that many students use unauthorized sources for finding solutions to assignments (such as course-hero, or copying solutions of fellow classmates). Under these circumstances giving credit for assignments raises fundamental issues of fairness and undermines our goal of upholding the highest possible standards of academic integrity.
  2. A huge amount of resources ends up being devoted to grading solutions that students copied. These resources can be better used to provide additional feedback on assignments and extra office hours.
  3. Students focus on trying to get the "right answer" rather than learning from assignments. Understanding why some idea is wrong is an important part of the learning process.
  4. There is often no single right answer to a solution and we want to encourage students to be creative.
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.
Midterm Exams:

There will be two in-class midterms on the following dates:

If you cannot make it at that date, please contact your instructor as soon as possible.

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%

The Piazza participation score will be based on the number of posts read, contributions, and endorsed answers.

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.