14356 - Differentiable Optimization Modulübersicht

Module Number: 14356
Module Title:Differentiable Optimization
  Differenzierbare 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 successful completion of the module, students know the problem types of differentiable optimization as well as the theory and procedures of differentiable optimization. They can create and evaluate different formulations of a problem, as well as select and evaluate appropriate procedures.
By working out a project, they have gained experience in independent scientific work. By presenting the results to the group, they have learned how to present and communicate mathematical results.
Contents:Unrestricted optimization
Optimality criteria, sensitivity, line search methods (e.g. gradient methods, CG methods, Newton methods, Quasinewton methods) and trust region methods, as well as their globalisations

Restricted optimization
Karush-Kuhn-Tucker theory (first and second order constraints, regularity), sensitivity, penalty and barrier methods, augmented Lagrangian methods, Lagrangian-Newton methods, SQP methods, nonlinear interior point methods
Studnets gain experience in independent scientific work by working out a project, and learn how to present and communicate mathematical results by presenting the results to the group.
  • Development of a project (independent scientific work)
  • Presentation of the results to the group (presentation and communication of mathematical results)
Recommended Prerequisites:Knowledge of the content the modules 
  • 11103: Analysis I
  • 11104: Analysis II
  • 11101: Lineare Algebra und analytische Geometrie I
  • 11102: Lineare Algebra und analytische Geometrie II
  • 13862: Optimierung und Operations Research
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:
  • W. Alt: Nichtlineare Optimierung. Vieweg, 2002.
  • C. Geiger, Ch. Kanzow: Numerische Verfahren zur Lösung unrestringierter Optimierungsaufgaben. Springer, 1999.
  • F. Jarre, J. Stoer: Optimierung. Springer, 2004.
  • J. Nocedal, S. Wright: Numerical Optimization. Springer, 1999.
  • M. Ulbrich, S. Ulbrich: Nichtlineare Optimierung. Springer, 2012
Module Examination:Prerequisite + Final Module Examination (MAP)
Assessment Mode for Module Examination:Prerequisite:
  • Successful completion of a project
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 Mathematik B.Sc.: Compulsory elective module in complex „Vertiefung“
  • Study programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in complex „Vertiefung“
  • Study programme Physics B.Sc.: Compulsory elective module in the basic study period
  • Study programme Informatik B.Sc.: Compulsory elective module in field of application „Mathematik“
  • Study programme Informatik M.Sc.: Compulsory elective module in "Mathematik“ or in field of Application „Mathematik“
  • Study programme Künstliche Intelligenz B.Sc.: Compulsory elective modul in complex „Mathematik“
  • Study programme Artificial Intelligence M.Sc.: Compulsory elective modul in complex „Learning and Reasoning"
  • Study programme Mathematics M.Sc.: Compulsory elective modul in complex „Optimization"
Module Components:
  • Lecture: Differentiable Optimization
  • Accompanying exercise
  • Related examination
Components to be offered in the Current Semester:
  • no assignment