MATHEMATICAL PROGRAMMING

Math 417 / 487 / 699 - Fall 2012.

General Information. (We are trying the new online system, so students should check there for the most uptodate info)

  • Overview
  • Course Instructor
  • Teaching Assistant
  • Lectures
  • Prerequisites
  • Textbooks
  • Course Notes and Materials
  • Assignments

    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 polytime algorithms for LP such as the Ellipsoid method and interior point methods. We present fundamental algorithms for integer programming Branch and Bound and Gomory's algorithm. Exploring integer programming more deeply, we give an overview of convex analysis including the theory of cutting planes. We also study topics in nonlinear programming including optimality conditions, convex programming and an introduction to geometric programming. We introduce topics in optimization with uncertain data such as robust optimization and stochastic programming.

    Math 699 is an associated reading course which will require extra lectures and work and is by departmental permission only.

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    Pre-requisites.

    Students should know the basics from Calculus and Linear Algebra. If you have doubts, please contact the instructor.

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

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    Instructor.

  • Prof. Bruce Shepherd
  • Telephone: 398-4578
  • Office: Room 1113, Burnside Building
  • Office hours: Thursday 130-3, or by appointment.
  • Email: bruce.shepherd at mcgill dot ca
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    Teaching Assistant.

    TBA
  • Atefeh Mohajeri
  • Office:
  • Office hours: Mon and Wed, 2-3 PM
  • Email: mohajeri at math.mcgill.ca
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    Lectures.

  • Time: Wednesday and Friday 10:00 - 11:30.
  • Location: Room 1B23, Burnside Hall
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    Textbooks.

    The text for the first 2/3 of the course is: Applied Mathematical Programming by Bradley, Hax, and Magnanti (Addison-Wesley, 1977)

    This covers most of the material on LP and Integer Programming. Extra material will be assigned when we discuss other topics such as cutting planes, stochastic programming, geometric programming etc.

    Course Notes and Materials

    A brief summary of lectures (i.e., a sparse Course Notes document) will be provided as we proceed.
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    Assignments.

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