This entry is from Winter semester 2021/22 and might be obsolete. No current equivalent could be found.

# Stochastic Optimization (dt. Stochastische Optimierung)

 Level, degree of commitment Specialization 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 Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics. Origin M.Sc. Mathematics Duration,frequency One semester, Im Wechsel mit anderen specialization 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.

## Applicability

The module can be attended at FB12 in study program(s)

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

When studying M.Sc. Mathematics, this module can be attended in the study area Specialization Modules in Mathematics.

The module can also be used in other study programs (export module).

The module is assigned to Applied Mathematics. Further information on eligibility can be found in the description of the study area.