Mathematical Programming

Objectives: Many problems arising from different domains can be formulated as linear and integer programs. The aim of this course is to study the modelisation and resolution techniques for these problems, based on linear and integer programming. We will introduce the main theoretical and algorithmic tools necessary for understanding and applying these techniques. We will also present some real applications to illustrate the algorithms that will be discussed.

Contents:

• Integer programming models

• Relation between linear programming and combinatorial optimization problems.

• Separation and optimization

• Cutting plane methods

• Decomposition techniques

• Applications

Bibliography:

• W. Cook, W. Cunningham, W.R. Pulleyblank, A. Schrijver, "Combinatorial Optimization", Wiley (1997).

• G. L. Nemhauser and L. A. Wolsey, " Integer and Combinatorial Optimization", Wiley (1988).

• L. A. Wolsey, Integer Programmation, Wiley (1998).

• A. Schrijver, "Theory of Linear and Integer Programming", Wiley (1998).