Fall 2019 - MATH 308 D200
Linear Optimization (3)
Class Number: 10765
Delivery Method: In Person
Course Times + Location:
Tu 4:30 PM – 5:20 PM
SWH 10041, Burnaby
Th 3:30 PM – 5:20 PM
SWH 10041, Burnaby
Exam Times + Location:
Dec 13, 2019
3:30 PM – 6:30 PM
WMC 3520, Burnaby
Prerequisites:MATH 150, 151, 154, or 157 and MATH 240 or 232.
Linear programming modelling. The simplex method and its variants. Duality theory. Post-optimality analysis. Applications and software. Additional topics may include: game theory, network simplex algorithm, and convex sets. Quantitative.
Couse topics: Theory and applications of linear programming, geometric and computational considerations, networks, applications of duality.
Outline:1. Linear Programming.
Examples - formulation of optimization problems as linear programming problems. Canonical forms for linear programming problems. Polyhedral convex sets.
2. The Simplex Algorithm.
Tucker Tableaus. The simplex algorithm for maximum tableaus and minimum tableaus. Cycling.
3. Noncanonical Linear Programming Problems.
Unconstrained variables. Equations as constraints.
4. Duality Theory
The dual simplex algorithm. Complementary slackness. The duality theorem.
5. Application: Matrix Games.Linear Programming formulation of matrix games. The von Neumann minimax theorem.
6. Other applications (as time permits).
- Honmework 15%
- Midterm Exam 35%
- Final Exam 50%
THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks. Please pay careful attention to the options discussed in class at the beginning of the semesters.
Attendance: Lecture attendance is required, and tutorial attendance is strongly encouraged. In the event that you miss a class, it is your responsibility to get the material from another student.
Homework: Homework assignments will be announced in lectures and will also be posted on canvas. They should be completed by the indicated due dates. Homework will be collected in lecture on the due dates. Late homework submission will not be accepted. If you are unable to submit your homework in the lecture for some understandable reasons, you should contact me in advance to see if you are allowed to submit it before the due date. The homework assignments will comprise substantial portion of your grade and you will be expected to take them seriously and to write them up neatly. Zero point will be given for those who copy or duplicate the others' homework or work. Please make every effort to complete all the assigned exercises. The assigned exercises will be also used as a resource for constructing your exams.
Exams: There will be one midterm exam as well as one final exam. The midterm exam is tentatively scheduled in lecture on October 24th (Wednesday). NO makeup exam will be given. A missed midterm exam, due to your own health related problems, will have its percentage added to the final exam, provided a medical certificate is received.
Linear Programming and Its Applications
Strayer, James K.
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