Nonlinear Optimization

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, cone-constrained optimization)

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.

MA0001 Analysis 1, MA0002 Analysis 2, MA0004 Linear Algebra 1, MA0005 Linear Algebra 2 and Discrete Structures, MA2012 Einführung in die Optimierung
(Former modules: MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra and Discrete Structures 1, MA1102 Linear Algebra and Discrete Struktures 2, MA2503 Introduction to Nonlinear Optimization, recommended: MA2504 Linear and Convex Optimization)
Für Studierende für Lehramt an Gymnasien: MA1005 Analysis 1 LG, MA1006 Analysis 2 LG, MA1105 Linear Algebra 1 LG, MA1106 Linear Algebra 2 LG, MA1107 Discrete Structures LG, MA2012 Einführung in die Optimierung
(Former modules: MA9935 Einführung in die Mathematik 1 LG, MA9936 Einführung in die Mathematik 2 LG, MA9937 Analysis 1 LG, MA9938 Analysis 2 LG, MA9939 Lineare Algebra 1 LG, MA9940 Lineare Algebra 2 LG, MA2503 Introduction to Nonlinear Optimization, recommended: MA2504 Linear and Convex Optimization)

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.

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Ulbrich, Ulbrich: Nichtlineare Optimierung, Birkhäuser, 2012.
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.
Jarre, Stoer: Optimierung, Springer, 2003.

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.