Lecture Mathematical Optimization

Goal

Introduction to advanced topics in optimization theory and algorithms. The course "Mathematical Optimization" gives the background knowledge to attend various special state-of-the-art lectures at IFOR like "Geometric Integer Programming".

Target Audience

Students with a mathematical interest in optimization. This course assumes the basic knowledge of linear programming, which is taught in courses such as "Introduction to Optimization".

Topics

• Integer optimization: Ties between linear and integer optimization, complexity theory, cutting plane theory.
• Combinatorial optimization: Structural results and algorithms for matroids, matchings and more generally, independence systems.
• Nonlinear optimization: Lagrange relaxation techniques, Newton method and gradient schemes for convex optimization.

Excercises

Information concerning the exercises and the certificate (Testat) condition can be found here.

CPLEX Web Interface

Click here to access the CPLEX-Solver.

References

Linear and Mixed Integer Linear Optimization

• Optimization over Integers. D. Bertsimas, R. Weismantel. Dynamic Ideas, 2005.
• Theory of Linear and Integer Programming. A.Schrijver. John Wiley, 1986.

Combinatorial Optimization

• Combinatorial Optimization. C.H. Papadimitriou. Prentice-Hall Inc., 1982.

Nonlinear Optimization

• Introductory Lectures on Convex Optimization: a Basic Course. Y. Nesterov. Kluwer Academic Publishers, 2003.