Math 407 Sections A and B Autumn 2016
LINEAR OPTIMIZATION
Instructor: James Burke          E-Mail: jvburke(at)uw(dot)edu
Phone: 543-6183          Office Hours: MW 1:30-2:30pm
Office: C-443 Padelford          & by appointment
Pre-Requisites: Math 308          Classroom: SAV 131
TA: Abraham Engle          Office: C-430 Padelford (PDL)
E-Mail: aengle2(dot)uw(dot)edu          Hours: TH. 3-5pm
         C-306 PDL, Math Library

URL for the course website:

Text:

Online course notes: http://www.math.washington.edu/~burke/crs/407/notes/

Course Content:

Math 407 is an introductory course in linear optimization with a focus on linear programming (or LP), quadratic optimization, and least-squares. The four basic components of the course are modeling, solution methodology, duality theory, and sensitivity analysis. Modeling concerns the question of how problems posed in the real world can be formulated in terms of the mathematical framework called linear programming. Solution methodologies concern practical techniques for computing the solution of an LP. We focus on the simplex algorithm due to George Dantzig since it offers a complete framework for discussing both the geometry and duality theory for linear programs. Duality theory illustrates the rich underlying mathematical structure of linear programming and its extensions. We will interpret the duality theory in a number of ways. In particular, we show how it can be used to explain pricing systems in market economies. Sensitivity analysis concerns the behavior of the optimal solution subject to changes in the initial data describing the problem.

The final topic in the course concerns the optimization of quadratic functions with a focus on linear least-squares problems. Here we consider the great variety of problems that can be modeled withing this framework. Our numerical investigations focus on properties of symmetric matrices and orthogonal projections.

Grading:

Quizzes: There are 8 fifteen minute quizzes each worth 80 points. The quizzes are given each Friday except Friday October 28, November 11 and 25, and December 9. There will aslo be a quiz on Wednesday, November 9. The quizzes cover the homework of the previous week. The potential content of the quiz will be announced the Wednesday before the quiz. Each quiz will contain two questions. The first question will either be to recite the definition of a vocabulary word or to formulate a problem as an LP. The second question will be computational in nature. The first quiz is manditory for all students enrolled in this class. The grade on the first quiz, as well as the top 4 scores on the remaining quizzes count toward your grade. In total, 5 quiz scores count toward your grade.

Midterms: There is one midterm: Wednesday, October 26. The content of the midterm will be discussed in advance and a sample midterm will be distributed before the exam. The midterm is worth 250 points.

Final Exam: The final exam for 407A is to be given on Monday, December 12, 8:30-10:20am, and that for 407B on Wednesday, December 14, 2:30-4:30pm. Both final exams will be given in SAV 131. The final exam is comprehensive. A sample final exam will be distributed. The final exam is worth 350 points.

Final Grade: The total number of possible points is 1000:

400 quiz points + 250 midterm points + 350 final exam points = 1000 points.
Your final grade will be based on these points. Note that the quiz grades count for 40% of your grade with the first quiz counting for 8%! One class curve is computed after the final exam has been scored.

Time Conflicts with an Exam:

There will be no make-up quizzes or exams except in the case of a documented emergency (medical, family, University, ...), or a documented unavoidable conflict whose validity is pre-authorized by the instructor. For unavoidable pre-approved conflicts, the instructor requires at least one week notice prior to the exam or quiz so that it can arrange for you to take the exam or quiz BEFORE the actual exam date.

Incomplete:

A grade of Incomplete will be given only if a student is doing satisfactory work up until the end of the quarter, and then misses the final exam due to a documented medical or family emergency.

Important Dates:

Holidays: Veterans Day, Friday, November 11: Thanksgiving, Thursday-Friday, November 24-25.

Midterm Date: Wednesday, October 26.

Final Exam: 407A: Monday, December 12, 8:30-10:20am: 407B: Wednesday, December 14, 2:30-4:20pm.