Math 417 / 487 - Fall 2011

Overview

We will give a thorough introduction to the main areas of mathematical programming. We start by studying linear programming (LP) including modelling, the Simplex Algorithm, sensitivity analysis, parametric programming and economic applications. We also discuss briefly polynomial-time algorithms for linear programming such as the ellipsoid method and interior point methods. We give an overview of convex analysis to support our handling of integer programming, including cutting plane theory. We also study topics in nonlinear programming including optimality conditions, convex programming and an introduction to geometric programming. We plan to also give an introduction to optimization under uncertainty, including robust optimization and stochastic programming.

Pre-requisites

Students should know the basics from Calculus and Linear Algebra.

NOTE: Math 417/487 may be used as a pre-requisite for Discrete Optimization II

Instructor

  • Yori Zwols
  • Office: Burnside 1243
  • Office hours: Thursdays 3pm-5pm
  • Email: yori dot zwols at mcgill dot ca

Lectures

  • Time: Wednesday and Friday 10:05 AM - 11:25 AM.
  • Location: Burnside Hall 1B23

Textbooks

The main course text is: Applied Mathematical Programming by Bradley, Hax, and Magnanti (Addison-Wesley, 1977)

This covers almost all of our material on LP and Integer Programming. Extra material will be assigned when we discuss other topics such as stochastic programming, geometric programming etc.

Course Notes and Materials

  • Course Notes (I will try to post updated notes after every lecture)

Assignments

Course grades will be based upon assignments (20%), midterm (30%) and a final exam (50%).

Assignment #1 (due Wednesday September 14th at the beginning of class)

  • Math 417: Exercises 1, 5, 6, 25, 28 from the textbook; Exercises 1, 2 from the notes.
  • Math 487/Mining students: Exercises 1, 5, 6, 7, 25, 26, 28 from the textbook; Exercises 1, 2 from the notes.
  • Solutions

Assignment #2 (due Wednesday October 5th at the beginning of class)

Assignment #3 (due Friday October 21st at the beginning of class)

Midterm

Assignment #4 (due Friday November 11th at the beginning of class)

Assignment #5 (due Friday December 2nd at the beginning of class)