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Nonsmooth Analysis and Optimization
(dt. Nichtglatte Analysis und Optimierung)

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements		 9 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Oral examination (individual examination) or written examination
Language,
Grading		 English,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Business Mathematics.
Duration,
frequency		 One semester,
irregular
Person in charge of the module's outline Prof. Dr. Patrick Mehlitz

Contents

Translation is missing, sorry. German original:

  • Einführung in die nichtglatte Optimierung.
  • Nichtglatte Variationsanalysis nach Mordukhovich: verallgemeinerte Normalenrichtungen und Subdifferentiale.
  • Numerische Lösung nichtglatter Optimierungsprobleme: Proximal-Gradienten-Verfahren, proximales Multiplikator-Straf-Verfahren, ADMM.
  • Numerische Lösung nichtglatter Gleichungssysteme: Newton-Differenzierbarkeit, lokale und globale Konvergenztheorie.

Qualification Goals

Translation is missing, sorry. German original:

Die Studierenden

  • verstehen die Notwendigkeit der Betrachtung nichtglatter Funktionen in der mathematischen Optimierung und können diese beispielhaft belegen,
  • können die Bedeutung zentraler Begriffe darstellen und in der Diskussion von nichtglatten Optimierungsproblemen und Gleichungssystemen erkennen,
  • können Methoden der nichtglatten Optimierung erläutern,
  • können nichtglatte Abbildungen auf anwendungsspezifische Weise in verallgemeinertem Sinn differenzieren,
  • können komplexere mathematische Arbeitsweisen (Entwicklung mathematischer Intuition und deren formale Begründung, Abstraktion, Beweisführung) anwenden,
  • sind in der Lage, fachliche Themen frei vor einem fachlichen Publikum vorzustellen und zu diskutieren.

Prerequisites

None. The competences taught in the following modules are recommended: either Linear Algebra I and Linear Algebra II and Analysis I and Analysis II or Basic Linear Algebra and Basic Real Analysis and Basics of Advanced Mathematics. In addition, knowledge of Continuous Optimization is an advantage.


Applicability

Module imported from M.Sc. Business Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • B.Sc. Business Mathematics
  • M.Sc. Data Science
  • M.Sc. Mathematics
  • M.Sc. Business Mathematics

When studying B.Sc. Business Mathematics, this module can be attended in the study area Free Compulsory Elective Modules.


Recommended Reading

  • Klatte, D., Kummer, B.: Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications, Springer, 2002
  • Mordukhovich, B.: Variational Analysis and Applications, Springer, 2018
  • Rockafellar, R.T., Wets, R.J.-B-: Variational Analysis, Springer, 1998



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2025/26. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

  • Winter 2016/17 (no corresponding element)
  • Summer 2018 (no corresponding element)
  • Winter 2018/19 (no corresponding element)
  • Winter 2019/20 (no corresponding element)
  • Winter 2020/21 (no corresponding element)
  • Summer 2021 (no corresponding element)
  • Winter 2021/22 (no corresponding element)
  • Winter 2022/23 (no corresponding element)
  • Winter 2023/24 (no corresponding element)
  • Winter 2025/26

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.