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Optimization I
(dt. Optimierung I)

Level, degree of commitment Advanced module, depends on importing study program
Forms of teaching and learning,
workload		 Lecture (3 SWS), recitation class (1 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements		 6 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination (individual examination)
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Business Mathematics.
Subject, Origin Mathematics, B.Sc. Business Mathematics
Duration,
frequency		 One semester,
Im Wechsel mit anderen specialization moduleen zur Optimierung
Person in charge of the module's outline Prof. Dr. Christian Rieger

Contents

Convex calculus and geometry (generalized derivation terms, tangent and normal cones, etc.) and, where appropriate, terms from nonconvex nonsmooth calculus and geometry.


Qualification Goals

Students will

  • know basic concepts of convex calculus in finite dimensions, which are especially important for the development of numerical optimization algorithms of nonsmooth convex problems,
  • understand nonsmooth calculus from F. Clarke's point of view in finite dimensions (directional derivative, subdifferentials, calculus rules) and its application in the development of efficient numerical optimization algorithms of nonsmooth nonconvex problems,
  • are familiar with the formulation, implementation and convergence analysis of important algorithms in nonsmooth optimization,
  • re-evaluate their knowledge from the basic modules and some advanced modules, e.g., from the calculus and linear algebra modules and the optimization modules,
  • recognize the relationships to other areas of mathematics and to other sciences,
  • have practiced mathematical ways of working (developing mathematical intuition and its formal justification, abstraction, proof),
  • have improved their oral communication skills in exercises by practicing free speech in front of an audience and in discussion.

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.


Recommended Reading

  • Will be announced in the module announcement.



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2023/24. 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

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.