14726 - Mathematical Optimization Techniques and Applications Modulübersicht

Module Number: 14726
Module Title:Mathematical Optimization Techniques and Applications
  Mathematische Optimierungstechniken und Anwendungen
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. habil. Fügenschuh, Armin
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: Every winter semester
Credits: 6
Learning Outcome:Upon successful completion of the module, students will have acquired an understanding of core mathematical tools used in modern optimization. They will be able to identify optimization structures in real-world problems, formalize these problems in mathematical terms, and apply suitable algorithms to obtain and interpret solutions. 
Contents:Foundations of optimization theory, global vs. local optimality, geometry of optimization, optimization for graph problems, fundamentals of linear programming, duality principles, advanced simplex methods, discrete optimization, interior point and ellipsoid methods, nonlinear optimization, applied modeling.
Emphasis is placed both on theoretical insights and algorithmic implementation.
Recommended Prerequisites:Knowledge of subject matters of the modules
  • 11103: Analysis I
  • 11104: Analysis II
  • 11101: Lineare Algebra und analytische Geometrie I
or of the modules
  • 11112: Mathematik IT-1 (Diskrete Mathematik)
  • 11113: Mathematik IT-2 (Lineare Algebra)
  • 11213: Mathematik IT-3 (Analysis)
Mandatory Prerequisites:
  • No successful participation in module 13862 Optimierung und Operations Research.
Forms of Teaching and Proportion:
  • Lecture / 4 Hours per Week per Semester
  • Exercise / 2 Hours per Week per Semester
  • Self organised studies / 90 Hours
Teaching Materials and Literature:
  • V. Chvatal, Linear Programming, Bedford St Martins Pr 3PL, 2016
  • R.J. Vanderbei: Linear Programming - Foundations and Extensions, 5th Edition, Springer, 2020
Module Examination:Continuous Assessment (MCA)
Assessment Mode for Module Examination:
  • 4 intermediate tests of 30 minutes each, written during the lecture period.
The best 3 count 1/3 each for the final grade.
Evaluation of Module Examination:Performance Verification – graded
Limited Number of Participants:None
Part of the Study Programme:
  • Master (research-oriented) / Mathematical Data Science / PO 2025
  • Master (research-oriented) / Mathematics / PO 2025
  • Master (research-oriented) / Physics / PO 2021
Remarks:
  • Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in complex „Optimierung"
  • Study programme Mathematics M.Sc.: Compulsory elective module in complex „Optimization"
  • Study programme Mathematical Data Science M.Sc.: Compulsory elective module in complex „Advanced Mathematical Methods in Data Science"
  • Study programme Artificial Intelligence Science M.Sc.: Compulsory elective module in complex „Advanced Methods"
  • Study programme Physics M.Sc.: Compulsory elective module in complex „Minor Subject"
Module Components:
  • Lecture: Optimization and Operations Research
  • Accompanying exercise
Components to be offered in the Current Semester:
  • no assignment