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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

  • Introduction to non-smooth optimization.
  • Non-smooth variational analysis according to Mordukhovich: generalized normal directions and subdifferentials.
  • Numerical solution of nonsmooth optimization problems: proximal gradient method, proximal multiplier penalty method, ADMM.

Numerical solution of non-smooth systems of equations: Newton differentiability, local and global convergence theory.


Qualification Goals

The students

  • understand the necessity of considering non-smooth functions in mathematical optimization and can prove this using examples,
  • can describe the meaning of central terms and recognize them in the discussion of non-smooth optimization problems and systems of equations,
  • can explain methods of non-smooth optimization,
  • can differentiate non-smooth mappings in an application-specific way in a generalized sense,
  • can apply more complex mathematical working methods (development of mathematical intuition and its formal justification, abstraction, proof),
  • are able to present and discuss technical topics freely in front of a professional audience.

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. Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.


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.