OR 641/MATH 689 - Linear Programming

Fall 2003, Tuesday 4:30-7:10, Aquia Module 103

Professor
Ariela Sofer
Professor and Chair
Science and Technology II, Room 111
phone: (703) 993-1692 or 993-1670 (secretary)
Office hours: Tuesday 2:30--4:00, Wednesday 2:30--4:00, or by appointment
electronic mail: asofer@gmu.edu
fax: (703) 993-1521 (on cover sheet put: A. Sofer, SEOR Dept.)

Text
Stephen G. Nash and Ariela Sofer, Linear and Nonlinear Programming, McGraw-Hill, (1996).

Course description
Linear programming problems arise in a wide variety of applications from areas such as finance, transportation, and military. These problems may be very large, potentially involving thousands of constraints and millions of variables. This course focuses on the theory and methods for solving large-scale linear programs. Students will gain hands-on experience in solving large-scale linear programs via computational work with the software CPLEX.

We will take an indepth look at the geometry of linear programs, then discuss the simplex method, duality theory and the dual simplex. We then discuss computational enhancements to the simplex that make it suitable for large sparse programs. These include the revised simplex, basis factorization, and bounded-variable linear programs. We then discuss computational complexity of finite algorithms, and in particular the simplex method. Finally, we discuss nonsimplex methods for linear programming including the ellipsoid method and the primal-dual interior-point method. The course will cover Chapters 2-7, 9, and Appendix A.1-A.5 of the book.

Grading
There will be an in-class midterm examination, and a cumulative final exam . The midterm will make up 25% of the grade and the final exam will make up 35% of the grade. Homeworks will make up 20% of the grade. A computational project will make up the remaining 20% of the grade. In computing the final grade, the lowest homework grade will be dropped. The exams will be open book, open notes.

Course Materials

Homework to date

Project

Make up Mid term Exam (pdf format)

Exam Dates
Midterm: Tuesday October 21
Final exam: Tuesday December 9, 4:30- 7:15.

Fundamental rules

• Make-up exams will only be given for extreme situations, and only if I am contacted before the exam is given and full arrangements are established. Full adherence to this policy is the responsibility of the student.
• The exam dates above are tentative, and it is the students responsibility to keep abreast of changes.
• Homework will be assigned each class, and usually collected. All work must be clearly written. Illegible work will not be accepted.
• There will be a penalty of 10% of the total grade for every day homework is late.