VL Optimization of Complex Systems

Contents

• News
• Lectures
• Contact
• General Information
• Registration
• Tutorial and Certificates
• Homework
• Literature

News

Lectures

Lecture	Wed. 12:15 - 13:45	Geom H2
	Fri. 12:15 - 13:45	Geom H2
Tutorial	Fri. 10:15 - 11:45	Geom 434

Contact

Dr. Anton Schiela	Geomathikum, Raum 123
	e-mail: schiela(at)zib.de

General Information

Contents of the Lecture

Content of this lecture are analysis and numerical solution of optimization problems, where complex physical processes, usually modelled by (partial) differential equations, have to be taken into account.
In contrast to classical finite dimensional optimization, these problems have an inherent infinite dimensional structure, due to the presence of differential equations. Thus, their analysis requires a mixture of functional analytic tools are techniques from optimization, and their efficient numerical solution involves the combination of algorithms and discretization methods.
Aim of this lecture is to give an introduction to this lively research topic in which analysis, optimization and numerics meet.

Topics

• Theory and Numerics of Optimization in Function Space
• Applications to Partial Differntial Equations
• Optimal Control of Partial Differential Equations

Registration

Registration

Tutorial and Certificates

Homework:

• There is a weakly homework sheet, which is distributed during the lectures on wednesday. They are also available at Stine
• All exercises may be solved in teams of at most two people.
• Homeworks are collected during the lecture on wednesday. Deadline is the end of the lecture 13:45.

Examn:

• At the end of the term there is an oral examn, which has to be passed to get a certificate. Condition for participation is that at least 50% of the homework credit points have been reached.
• Date and time of the examn are shortly after the end of the semester. The exact date is to be announced.
• Certificates have a grade, according to the grade reached at the examn.

Criteria for the certificate:

• Active contribution in the tutorial
• 50 % of the total number of homework points
• Examn successfully passed

Sheets

Homework sheets in Portable Document Format (*.pdf) can be downloaded at Stine . New sheets are usually uploaded tuesday evening. Homework sheets in printed form are distributed during the wednesday lectures

Literature:

The lecture is not oriented at a particular book, but the following books cover wide parts of the content:

Hinze, Pinnau, Ulbrich, Ulbrich: Optimization with PDE Constraints
Tröltzsch: Optimal Control of Partial Differential Equations / Optimale Steuerung partieller Differentialgleichungen
Ekeland/Temam: Convex Analysis and Variational Problems

The following books cover analytic and numerical basics, but maybe you have a different favourite book on these topics:

Rudin: Functional Analysis
Rudin: Real and Complex Analysis (good introduction to integration)
Conway: A Course in Functional Analysis
Werner: Funktionalanalysis
Werner: Einführung in die Höhere Analysis (brief account of topology, integration, functional analysis)
Braess: Finite Elements / Finite Elemente
Ciarlet: The Finite Element Method for Elliptic Problems (classic in finite element theory)
Deuflhard: Numerical Analysis in Modern Scientific Computing I / Numerische Mathematik I (numerical basics)
Nocedal/Wright: Numerical Optimization (finite dimensional optimization)
Adams: Sobolev Spaces (reference book for Sobolev spaces)

The following books contain further reading and may be of interest to you in the future

Zeidler: Applied Functional Analysis v. 108/109
Zeidler: Nonlinear Functional Analysis and its Applications I-IV, in particular III
Borwein/Zhu: Techniques of Variational Analysis
Dacorogna: Direct Methods in the Calculus of Variations
Struwe: Variational Methods
Ito/Kunisch: Lagrange Multiplier Approach to Variational Problems and Applications