# 101.804 AKNUM Optimization and shape optimization with partial differential equations This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2022W 2019W

2022W, SE, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: SE Seminar
• Format: Presence

## Learning outcomes

After successful completion of the course, students are able to understand and solve shape optimization problems and/or optimal control problems contstrained by partial differential equations. Students will have gained an overview over optimisation and shape optimisation with partial differential equations.

## Subject of course

We discuss selected topics in optimisation and shape optimisation with partial differential equations. The focus is on both theory and numerics and possible topics can be

• `shape optimization with shape manifolds`
• `shape spaces`
• `nonsmooth shape optimization`
• `quasi-Newton methods`
• `shape optimization with the Minkowski sum`
• `semi-smooth Newton methods`

Applications of shape optimization are for instance car and aircraft design, electrical machines, conductor design or medical imaging.

## Teaching methods

Presentation and if applicable implementation of algorithms

## Mode of examination

Oral

First meeting: Tuesday, 11.10.2022 Sem.R. DA grün 06A

Please consider the plagiarism guidelines of TU Wien when writing your seminar paper: Directive concerning the handling of plagiarism (PDF)

## Course dates

DayTimeDateLocationDescription
Tue11:00 - 12:0011.10.2022Sem.R. DA grün 06A Optimierung und Formoptimierung mit partiellen Differentialgleichungen

## Examination modalities

successful presentation

Not necessary

## Curricula

Study CodeObligationSemesterPrecon.Info
860 GW Optional Courses - Technical Mathematics Mandatory elective

## Literature

• `Tröltzsch - optimale steuerung partieller differentialgleichungen`
• `Delfour/Zolesio - Shape and geometries`
• `Ito/Kunisch -  Lagrange Multiplier Approach to Variational Problems and Applications`
• `Henro/Pierre - Optimisation de forme`
• `Nocedal/Wright - Numerical Optimization`
• `Sepulchre, Absil, Mahony - Optimization algorithm on matrix manifolds`
• `Kanzow, Geiger - Theorie und Numerik restringierter Optimierungsaufgaben`

## Previous knowledge

PDE and Numerik; for topics involving manifolds differential geometry is recommended

## Language

if required in English