Math 354: Linear Optimization

Spring 2022

Instructor: Kristen Hendricks

Email: kristen. hendricks at rutgers.edu

Office Hours: M 3-4 pm, Th 9-10 am on Zoom via Canvas integration.

TA: Jikang Wang

Email: jw1117 at rutgers.edu

Office Hours: W 2-3, F 4-5 on Zoom via Canvas integration.


Location and Time: Lecture MTh 12:10-1:30, over Zoom via Canvas integration until 1/30, possibly afterward at BRR-5101. Lectures over zoom will be recorded and videos and notes will be made available here.

Prerequisites:Math 250.

Texbook: S. Miller, Mathematics of Optimization: How To Do Things Faster. It may also be useful to consult B. Kolman and E. Beck, Elementary Linear Programming With Applications

Content: This course is an introduction to linear optimization. We will cover linear programming problems, the simplex method, duality theory and sensitivity analysis, integer programming, and various applications as time permits.

Homework: Homework will be assigned weekly and due on Thursday at 11 am via Canvas Assignments, except for the last assignment, which will be due on Monday May 3 at 11 am. There will be thirteen homeworks in total. No late homework will be accepted. However, your lowest three homework scores will be dropped when computing your grade.

Typically two homework problems will be graded carefully, and some points will be given for completeness of the rest of the assignment. Homework solutions will be posted online promptly.

You are encouraged to work in groups on your homework. However, you must write up all solutions yourself. Moreover, since crediting your collaborators is an important element of academic ethics, you should write down with whom you worked at the top of each assignment. You must also cite any sources you use other than the lecture or the textbooks (other textbooks, Mathematics Stack Exchange, doublechecking a graph using Desmos, etc.) You should not consult Chegg or other paid homework solutions sites.

Quizzes and Exams: There will be a thirty-minute quiz on Monday, February 7 and two eighty-minute midterm exams on Monday, February 28 and Monday, April 11. There will also be a final exam scheduled by the registrar. Exams will be taken closed book and closed notes. In the event that exams are not in-person, exam procedures will be announced a few days in advance. If you miss a quiz or midterm for a documented good reason (such as serious illness or other comparable emergency), your final will count for a higher percentage of your grade accordingly. Make-up finals will only be given in extreme circumstances.

Grading: Grades will be computed as follows:

A reasonable curve will be applied to the composite numerical scores. The bar for an A will not be set higher than an overall 90% in the course.



Assignments

Homework 1. Due January 27 at 11 am. Solutions.

Homework 2. Due February 3 at 11 am. Solutions.

Homework 3. Due February 10 at 11 am. Solutions.

Homework 4. Due February 17 at 11 am. Solutions.

Homework 5. Due February 24 at 11 am. Solutions.

Homework 6. Due March 3 at 11 am. Solutions.

Homework 7. Due March 10 at 11 am. Solutions.

Homework 8. Due March 24 at 11 am.Solutions.

Homework 9. Due March 31 at 11 am. Solutions.

Homework 10. Due April 7 at 11 am.Solutions.

Homework 11. Due April 14 at 11 am.Solutions.

Homework 12. Due April 21 at 11 am.Solutions.

Homework 13. Due May 2 at 11 am.Solutions.

Exam Materials

Sample Quiz. Solutions.

Quiz. Solutions.

Sample Midterm 1. Solutions.

Midterm 1. Solutions.

Sample Midterm 2. Solutions.

Midterm 2. Solutions.

Sample Final. Solutions.