*This course is taught in English. This course is regularly offered every winter semester.*

*This course was offered in the winter term 2021/22.*

Link official course page

#### Description

Optimisation is the selection of a best element from a set of available alternatives. Such problems are fundamental in our daily lives and arise in all quantitative disciplines from computer science and engineering to operations research and economics.

The aim of this course is to show the methodology for solving constraint optimisation problems both for linear and non-linear problems. These methodologies are also known as Linear and Non-Linear Programming, respectively. Special attention is paid to the application of these methodologies in practical problems ranging from transportation to portfolio optimisation. We will study in-depth how to take a practical problem and formulate it into a mathematical formulation. Then we introduce algorithms for solving these. Finally, theoretical foundations are underlying these algorithms are addressed to train intuition on applicability.

**ECTS-Points: 6**

#### Topics

- modelling linear programming problems
- graphical method
- algebraic background
- convexity
- polyhedral theory
- simplex method
- degeneracy and convergence
- duality
- interior-point methods
- quadratic optimization
- integer linear programming

#### Recommended literature:

- B. Guenin, J. Könemann, L. Tunçel: A gentle introduction to optimization. Cambridge University Press, 2014
- A. Schrijver: Combinatorial Optimization: Polyhedra and Efficiency. Springer, 2003
- B. Korte and T. Vygen: Combinatorial Optimization: Theory and Algorithms. Springer, 2018
- T. Cormen, Ch. Leiserson, R. Rivest, C. Stein: Introduction to Algorithms. MIT Press, 2013