* Students can find the right method to solve a given mathematical problem.
* Students can apply the linear and nonlinear optimization methods to concrete mathematical problems.
* Students can validate the method and the solution, depending on the mathematical problem.
* Students learn the concepts and solution method (the simplex method) for linear constrained optimization problems.
* Students can apply the linear optimization method to problems in game theory and network flow problems.
* Students learn the concepts and solution methods for nonlinear unconstrained and constrained optimization problems.
* Students learn the definition of concave and convex functions, their characterizations, and their importance in nonlinear optimization problems.
* Students can recognize concave and convex functions by applying their characterizations.
* Students can clearly present their solutions of mathematical problems in groups.

Optimisation problems arise in all fields that econometricians encounter, such as operations research, game theory, statistics, micro- and macroeconomics and finance. 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. The following topics and techniques will be treated: the standard simplex method, duality, sensitivity analysis, the primal-dual simplex method, the network simplex method, first and second order necessary and sufficient conditions, the Lagrangian-function, Kuhn-Tucker conditions and constraint qualification. Besides this, special attention is paid to the application of these methodologies in practical problems.

Vanderbei, R.J., Linear Programming: Foundations and Extensions, 5th edition, Springer, ISBN 978-3-030-39414-1 ISBN 978-3-030-39415-8 (eBook) https://doi.org/10.1007/978-3-030-39415-8

Basic algebra (for linear programming), and advanced calculus (for nonlinear programming).
Exchange students need to be aware that very specific pre-knowledge is required for this course. A solid background in mathematics is necessary. Students should be aware of the following concepts: Algebra: working knowledge of vector computing and matrices (including inverse matrices). Linear equations, and find the solutions of a set of equations etc.
Function theory on the level of optimisation of functions of multiple variables under side conditions (Lagrange multipliers)

An advanced level of English.