Linear and Discrete Optimization

This course serves as an introduction to linear and discrete optimization from the viewpoint of a mathematician or computer scientist.  Besides learning how linear and discrete optimization can be applied, we focus on understanding methods that solve linear programs and discrete optimization problems in a mathematically rigorous way.

We will answer  questions like:

• Does a particular method work correctly?
• Does it terminate and, if yes, in what time?
• Can we prove that a solution is optimal?

The course starts by discussing what a linear program is and how linear programming can be applied. Then, we will treat the simplex method and the theory of duality. We will then discuss some combinatorial optimization problems like maximum weight bipartite matching and maximum flows. 

The course constitutes about half of the material on linear and discrete optimization that is taught for mathematics and computer science undergraduates at EPFL and will feature video lectures, quizzes, programming assignments, and a final exam.

• Linear programming, modeling, equivalence of standard forms
• Basic solutions, primal and dual feasible basic solutions, pivoting and the simplex method
• Termination and complexity of the simplex method
• Integer programming, bipartite matching and flows
• Models of computation, bit-complexity