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German original

Non-smooth Optimization
(dt. Nichtglatte 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. Convex Analysis and Geometry

  • Basic concepts of convex analysis, in particular generalized derivatives, tangent and normal cones, calulus rules and relationships between the analytical and geometric concepts.

II. Nonconvex Nonsmooth Analysis and Geometry

  • Nonsmooth analysis in the sense of F. Clarke, Clarke's directional derivative, subdifferential, tangent and normal cones, calculus rules and relations between the analytical and geometric concepts.

III. Numerical Methods of Nonsmooth Optimization

  • Numerical solution algorithms for nonsmooth optimization problems, in particular subgradient methods and bundle methods for convex and nonconvex problems
  • The semi-smooth Newton method for non-smooth operator equations

Qualification Goals

The students shall

  • to receive a thorough introduction to the necessary concepts of convex analysis in finite dimensions, which are especially important for the development of numerical optimization algorithms for non-smooth convex problems,
  • learn the non-smooth analysis from the point of view of F. Clarke in finite dimensions (directional derivation, subdifferentials, calculation rules) and their application in the development of efficient numerical optimization algorithms for non-smooth nonconvex problems,
  • learn the formulation, implementation and convergence analysis of important algorithms in non-smooth optimization,
  • 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. In addition, knowledge of nonlinear optimization is an advantage.


Recommended Reading

(not specified)



Please note:

This page describes a module according to the latest valid module guide in Wintersemester 2020/21. 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.