Discrete Optimization - 1

 308-566A                    Autumn 2002     Leacock 14    TuTh 1-2:30pm

This course is concerned with the formulation and solution of linear programs and related geometrical problems. In the first part of the course, the basic foundation will be laid: problem formulation, the simplex method, duality theory, the revised simplex method, computer implementations, and integer programming. This part of the course will last about 5-6 weeks. The second part of the course will concern the interplay between linear programming and geometry and its application to networks and games. This part of the course will last about 2-3 weeks. The third part of the course will consist of a survey of some of the latest developments in linear programming, including polynomial time methods, and a study of selected applications of linear programming to solve both applied and theoretical problems. The topics selected will depend on the interests of the class. For the third part of the course, each student will be expected to prepare a class presentation (20 minutes) and written report on one such application. Depending on the class size, students may instead do a project involving an application of the techniques learned in the course, instead of the presentation.

There will be two  in-class tests worth 30% each, covering material given in the first two parts of the course. The presentation or project will count 20%, and the remaining 20% of the mark will be from 4 homework assignments. Some of the homework will involve computing. In particular, we will use  the symbolic computation packages MAPLE  as a tool in solving linear programs. Students will also have access to lp-solve and the commercial package CPLEX to solve larger problems.

Assignments are due in class. Late assignments should be given directly to the TA or left in my mailbox. Penalty: -10% per day, including weekends.

Prerequisites:  308-360 (or 308-405) and 189-223.

Required Text: Linear Programming, by V. Chvatal, W.H. Freeman

Texts on Reserve at Schulich Library:

- Linear Programming, by V. Chvatal
- Linear Programming, by J. Ignizio and T. Cavalier
- Integer Programming, by L. Wolsey

Instructor:  David Avis
McConnell 308  avis@cs.mcgill.ca http://www.cs.mcgill.ca/~avis
Office Hours: Tu, Th  11-12

Teaching Assistant: Bohdan Kaluzny (to be confirmed)
McConnell 232  beezer@cs.mcgill.ca http://www.cs.McGill.CA/~beezer
Office Hours: tba

Class Tests: tba, early October and November

August 23, 2002