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Nonlinear Optimization: Advanced

Module MA3503

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.

available module versions
SS 2012WS 2011/2

Basic Information

MA3503 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Catalogue of non-physics elective courses
Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions

Content

Examples of nonlinear optimization problems in practice, selected advanced topics in unconstrained optimization, constrained optimization (detailed development of optimality theory, development and analysis of important classes of numerical methods such as sequential quadratic programming, barrier methods, and interior point algorithms), selected further topics (e.g., robust optimization, sparsity-constrained optimization).

Learning Outcome

At the end of the module students are able to understand optimization theory in detail, to understand advanced theoretical and numerical aspects of modern nonlinear optimization, to assess and investigate the convergence properties of optimization methods and to apply optimization theory and methods.

Preconditions

MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra and Discrete Structures 1, MA1102 Linear Algebra and Discrete Structures 2, MA2503 Introduction to Nonlinear Optimization, Empfohlen: MA2504 Linear and Convex Optimization

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

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.

Media

blackboard

Literature

Lösung unrestringierter Optimierungsaufgaben, Springer, 1999.
Geiger, Kanzow: Theorie und Numerik restringierter Optimierungsaufgaben, Springer, 2002.
Nocedal, Wright: Numerical Optimization, Springer, 2006.
Jarre, Stoer: Optimierung, Springer, 2003.

Module Exam

Description of exams and course work

The module examination is based on a written exam (60 minutes). Students are able to understand the theoretical and numerical basics of nonlinear optimization and can adequately apply the methods and algorithms. They are able to analyze their convergence properties.

Exam Repetition

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

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