Advanced Linear Programming - M1 - 6EC

Prerequisites

  • Parts on Linear Programming in any book Introduction to Operations Research.
  • A course on Linear Algebra based on e.g. David C. Lay, Stephen R. Lay and Judi J. McDonald, Linear Algebra and its Applications. For mathematics students their knowledge of Linear Algebra should suffice to match up rather easily.
  • The course is organized by the Dutch Network for the Mathematics of Operations Research and as such meant, among others for Master students in Operations Research.

Aim of the course
To provide insight in the theory of linear optimization and in the design of advanced  practical methods for solving (integer) linear optimization problems.

Part 1: Basic theory and algorithms of linear optimization: - Linear optimization -  polyhedra and polytopes - the simplex algorithm - duality - linear inequalities and  Farkas' lemma – network flow problems – ellipsoid method and separation

Part 2: Advanced linear optimization methods - the revised simplex method and column generation - Dantzig-Wolfe and Benders' decomposition - integer  programming formulations and solution methods- valid inequalities- branch-and-cut.

Lecturers
Leen Stougie
Christopher Hojny