Courses Bachelor Display 20222023
Course Description  To PDF  

Course title  Optimisation  
Course code  EBC2105  
ECTS credits  6,5  
Assessment  Whole/Half Grades  
Period 


Level  Intermediate  
Coordinator 
Stan van Hoesel, Janos Flesch For more information: s.vanhoesel@maastrichtuniversity.nl; j.flesch@maastrichtuniversity.nl 

Language of instruction  English  
Goals 
* 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. 

Description 
PLEASE NOTE THAT THE INFORMATION ABOUT THE TEACHING AND ASSESSMENT METHOD(S) USED IN THIS COURSE IS WITH RESERVATION. A REEMERGENCE OF THE CORONAVIRUS AND NEW COUNTERMEASURES BY THE DUTCH GOVERNMENT MIGHT FORCE COORDINATORS TO CHANGE THE TEACHING AND ASSESSMENT METHODS USED. THE MOST UPTODATE INFORMATION ABOUT THE TEACHING/ASSESSMENT METHOD(S) WILL BE AVAILABLE IN THE COURSE SYLLABUS.
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 nonlinear problems. These methodologies are also known as Linear and NonLinear Programming, respectively. The following topics and techniques will be treated: the standard simplex method, duality, sensitivity analysis, the primaldual simplex method, the network simplex method, first and second order necessary and sufficient conditions, the Lagrangianfunction, KuhnTucker conditions and constraint qualification. Besides this, special attention is paid to the application of these methodologies in practical problems. 

Literature 
* Vanderbei, R.J., Linear Programming: Foundations and Extensions, 4th ed., Springer, 2014, ISBN 978146147629.
* Sydsaeter K, Hammond P, Seierstad A, Strom A (2008): Further mathematics for economic analysis. Essex UK, Prentice Hall (2nd edition). ISBN: 9780273713289. 

Prerequisites 
Basic algebra (for linear programming), and advanced calculus (for nonlinear programming).
Exchange students need to be aware that very specific preknowledge 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. 

Teaching methods (indicative; course manual is definitive)  PBL / Lecture  
Assessment methods (indicative; course manual is definitive)  Attendance / Participation / Written Exam  
Evaluation in previous academic year  For the complete evaluation of this course please click "here"  
This course belongs to the following programmes / specialisations 
