Math 16. Linear Programming

The final will be a take-home exam, handed out on Friday, May 26 and due on Wednesday, May 31.

This course provides an introduction to linear programming, a tool widely used in operations research. A linear programming problem deals with the optimization of a linear function subject to a number of constrains. The first objective of the course is to learn what a linear program is and to be able to recognize it in "real-world problems". We will learn how to solve linear programming problems using the simplex method. The study of the simplex method will involve duality theory, implementation issues, measuring the efficiency of the algorithms, and other related topics. We conclude the course with applications of linear programming to game theory and network flows. If time permits we will also address integer programming and interior point methods.

Linear Programming Foundations and Extensions by Robert J. Vanderbei. Second edition

This syllabus is subject to change, but it should give you an idea of the topics I want you to learn.

	Chapters	Brief Description
Week 1	1, 2	Linear Programming and the simplex method.
Week 2	2, 3	Simplex method and degeneracy
Week 3	3, 4	Analysis of the simplex method and the Dual problem.
Week 4	5	The dual problem and weak and strong duality theorems.
Week 5	6, 7, 8	Matrix notation, sensitivity analysis, implementation issues.
Week 6	10, 11	Convex analysis. Matrix games.
Week 7	11	Minimax theorem. Simplified poker.
Week 8	13	Network Flows Primal Network simplex Method.
Week 9	13	Primal/Dual network simplex method and applications of network flows.
Week 10	22 (tentative)	Integer Programming.

The course grade will be based on the homework (20%), two midterms (25% each), a final exam (25%), and class participation (5%).

There will be homework due every week. It will consist typically of a reading assignment (of the part of the book covered in class) and some problems. Collaboration in the homework is permitted, but you are not allowed to copy someone else's work. The solutions must be written individually. You have to mention on your problem set the names of the students that you worked with.

Exams

On the midterms and the final exam you must work on the problems on your own. No collaboration permitted in the exams.

Students with disabilities: Students with learning, physical, or psychiatric disabilities enrolled in this course that may need disability-related classroom accommodations are encouraged to make an office appointment to see me before the end of the second week of the term. All discussions will remain confidential, although the Student Disability Services office may be consulted to discuss appropriate implementation of any accommodation requested.