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# Introduction to Nonlinear Optimization

## Module MA2503

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Module version of SS 2012 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2012WS 2011/2

### Basic Information

MA2503 is a semester module in German language at Bachelor’s level which is offered in winter semester.

Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

### Content, Learning Outcome and Preconditions

#### Content

Modelling of practical problems as optimization problems, unconstrained optimization (optimality conditions, globally convergent descent methods, Newton method and Newton-type methods, globalization of locally convergent methods), elements of constrained optimization.

#### Learning Outcome

After successful completion of the module students are able to formulate practical problems as optimization problems as well as to understand and to apply the theoretical basics of nonlinear optimization.
Further, they understand modern optimization methods and elements of their convergence theory, and they are familiar with and can apply fundamental concepts in the theoretical analysis of nonlinear optimization problems.

#### Preconditions

MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Lineare Algebra 1, MA1102 Lineare Algebra 2

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

TypeSWSTitleLecturer(s)DatesLinks
VO 2 Introduction to Nonlinear Optimization [MA2503] May, S. Thu, 16:15–17:45, Interims I 102
documents
UE 1 Introduction to Nonlinear Optimization (Exercise Session) [MA2503] Christof, C. Hafemeyer, D. May, S. singular or moved dates
and dates in groups
eLearning
documents

#### Learning and Teaching Methods

The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress. At the beginning of the module, the practice sessions will be offered under guidance, but during the term the sessions will become more independent, and intensify learning individually as well as in small groups.

Black board

#### Literature

Geiger, Kanzow: Numerische Verfahren zur Lösung unrestringierter Optimierungsaufgaben, Springer, 1999.
Geiger, Kanzow: Theorie und Numerik restringierter Optimierungsaufgaben, Springer, 2002.
Nocedal, Wright: Numerical Optimization, Springer, 2006.

### Module Exam

#### Description of exams and course work

The module examination is based on a written exam (60 minutes). Students have to know the theoretical foundations of nonlinear optimization and modern optimization methods including their convergence theory. They can model practical tasks as optimization problems and give solution approaches.

#### Exam Repetition

The exam may be repeated at the end of the semester.

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