Mathematical Optimization Techniques and Applications
Mathematische Optimierungstechniken und Anwendungen
6 CPWinterEN
Prerequisites
Mandatory, as written
• No successful participation in module 13862 Optimierung und Operations Research.
Recommended, as written
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)
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.
Learning outcomes
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.
Assessment
• 4 intermediate tests of 30 minutes each, written during the lecture period. The best 3 count 1/3 each for the final grade.
Literature (2)
- V. Chvatal, Linear Programming, Bedford St Martins Pr 3PL, 2016
- R.J. Vanderbei: Linear Programming - Foundations and Extensions, 5th Edition, Springer, 2020
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 Künstliche Intelligenz Technologie M.Sc.: Compulsory elective module in complex „Software-basierte Systeme" • Study programme Physics M.Sc.: Compulsory elective module in complex „Minor Subject"
Source: BTU's module description · retrieved 29 Sep 2026Original