In this course the student will learn to solve both linear and non-linear constrained optmization problems.

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.

Course book.
Vanderbei, R.J., Linear Programming: Foundations and Extensions, 2nd ed., Kluwer Academic Publishers, 2001 (ISBN 0792381416 or ISBN 0792373421).

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 necessarry. 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.