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German original

Stochastic Optimization
(dt. Stochastische Optimierung)

Level, degree of commitment in original study programme Advanced module, compulsory elective module
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: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading
German,
The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.
Original study programme M.Sc. Mathematik / Vertiefungsbereich Mathematik
Duration,
frequency
One semester,
Im Wechsel mit anderen advanced moduleen zur Optimierung
Person in charge of the module's outline Prof. Dr. Thomas Surowiec

Contents

I. Models of Stochastic Optimization

  • A formal mathematical discussion of the modelling of different business-relevant applications, e.g. inventory problems, manufacturing and multi-product problems, portfolio optimization, logistics

II. Two-stage Stochastic Optimization

  • Theory of linear, polyhedral and general two-stage stochastic optimization problems, necessary concepts from nonlinear optimization and convex analysis, such as duality theory and Lagrange multipliers, the role of recourse in theory and numerics.

III. Numerical methods

  • L-shaped method, sampling-based methods such as stochastic quasi-gradient and stochastic decomposition

Qualification Goals

The students shall

  • learn how to model application-relevant problems with stochastic optimization problems,
  • learn the aspects of the theory of two-stage stochastic optimization problems, which are especially important for the development of numerical optimization algorithms,
  • learn the extension of concepts from linear and nonlinear optimization to stochastic optimization problems,
  • Reassess knowledge from the basic modules and some advanced modules, e.g. from the modules for analysis and linear algebra as well as the optimization modules,
  • recognise relations with other areas of mathematics and other sciences,
  • practice mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof techniques),
  • improve their oral communication skills in the exercises by practicing free speech in front of an audience and during 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, either Measure and Integration Theory or Elementary Stochastics.


Recommended Reading

(not specified)



Please note:

This page describes a module according to the latest valid module guide in Sommersemester 2021. 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:

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.