14264 - Special Topics of Infinite-Dimensional Optimization Modulübersicht

Module Number: 14264
Module Title:Special Topics of Infinite-Dimensional Optimization
  Spezielle Kapitel der unendlichdimensionalen Optimierung
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. habil. Wachsmuth, Gerd
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: On special announcement
Credits: 8
Learning Outcome: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.
Contents: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
Recommended Prerequisites:Knowledge of the content of the modules
  • 13862: Optimierung und Operations Research
  • 11303: Funktionalanalysis  or 13844: Functional Analysis
Mandatory Prerequisites:None
Forms of Teaching and Proportion:
  • Lecture / 4 Hours per Week per Semester
  • Exercise / 2 Hours per Week per Semester
  • Self organised studies / 150 Hours
Teaching Materials and Literature:
  • 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
Module Examination:Prerequisite + Final Module Examination (MAP)
Assessment Mode for Module Examination:Prerequisite:
  • Successful completion of exercises
Final module examination:
  • Oral examination, 30 min.
Evaluation of Module Examination:Performance Verification – graded
Limited Number of Participants:None
Part of the Study Programme:
  • no assignment
Remarks:
  • Study programme Mathematics M.Sc.: Compulsory elective module in complex "Optimization"
Module Components:
  • Lecture: Special Topics of Infinite-Dimensional Optimization
  • Accompanying exercises
  • Related examination
Components to be offered in the Current Semester:
  • no assignment