Special Topics of Infinite-Dimensional Optimization
Spezielle Kapitel der unendlichdimensionalen Optimierung
8 LPunregelmäßigEN
Voraussetzungen
Empfohlen, im Wortlaut
Knowledge of the content of the modules • 13862: Optimierung und Operations Research • 11303: Funktionalanalysis or 13844: Functional Analysis
Inhalte
Treatment of optimization topics in (infinite-dimensional) Banach spaces Existence of solutions Weak topologies, separation theorems, weak closedness, weak semicontinuity, verification of existence Necessary optimal conditions of first order Bipolar theorem, differentiation in Banach spaces, weak mean value theorem, Taylor expansion, tangent cones, normal cones, constraint qualifications, Lagrange multipliers Optimality conditions of second order Second-order derivatives, second-order Taylor expansion, second-order necessary conditions, second-order sufficient conditions, two-norm discrepancy
Lernziele
After successfully completing the module, students will be familiar with proofs of the existence of solutions. They can apply concepts from functional analysis. Students are able to derive and understand optimality conditions. In addition, they are able to present and communicate mathematical results by presenting their results to the group.
Prüfungsleistung
Prerequisite: • Successful completion of exercises Final module examination: • Oral examination, 30 min.
Literatur (4)
- Bonnans, J.Frederic, Shapiro, Alexander, Perturbation Analysis of Optimization Problems, Springer
- Ioffe Aleksandr D. und Vladimir M. Tichomirov, Theorie der Extremalaufgaben, VEB Deutscher Verlag der Wissenschaften
- Jochen Werner, Optimization, Theory and Applications, Vieweg-Verlag
- Dirk Werner, Funktionalanalysis, Springer, https://link.springer.com/book/10.1007%2F978-3-642-21017-4
Bemerkungen
• Study programme Mathematics M.Sc.: Compulsory elective module in complex "Optimization"
Quelle: Modulbeschreibung der BTU · abgerufen 15.10.2026Original