German original

# Nonlinear Optimization (dt. Nichtlineare Optimierung)

 Level, degree of commitment in original study programme Advanced module, compulsory elective module Forms of teaching and learning,workload Lecture (4 SWS), recitation class (2 SWS), 270 hours (90 h attendance, 180 h private study) Credit points,formal requirements 9 CP Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises. Examination type: Written or oral examination Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Business Mathematics. Original study programme M.Sc. Wirtschaftsmathematik / Mathematische Vertiefungs- und Praxismodule Duration,frequency One semester, Regelmäßig im Wechsel mit anderen Lehrveranstaltungen im Forschungsgebiet Optimierung Person in charge of the module's outline Prof. Dr. Thomas Surowiec

## Contents

Fundamentals of nonlinear optimization: Kuhn-Tucker theory, minimization of nonlinear functions; minimization of nonlinear functions with constraints

Fundamentals of nonlinear optimization: Kuhn-Tucker theory, minimization of nonlinear functions; minimization of nonlinear functions with constraints

## Qualification Goals

The students shall

• acquire a sound knowledge of the theory and practice of basic methods of optimization
• learn to recognize and assess the relevance of optimization methods for practical problems from different application areas such as parameter optimization, nonlinear regression, approximation, or optimal control,
• acquire the ability to model and solve optimization problems in practical situations,
• practice mathematical methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof methods),
• improve their oral communication skills in the recitation classes by practicing free speech in front of an audience and during discussion.

## Prerequisites

None. The competences taught in the following modules are recommended: either Linear Algebra I and Analysis I and Analysis II or Basic Linear Algebra or Basic Real Analysis and Basics of Advanced Mathematics.

• Alt, W.: Nichtlineare Optimierung, Vieweg, 2002
• Jarre, F., Stoer, J.: Nonlinear Programming, Springer, 2004
• Fletcher, R.: Practical Methods of Optimization, 2nd Edition, John Wiley & Sons, 1987
• Nocedal, J., Wright, S.: Numerical Optimization, Springer, 2002