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# The minimization of a maximum-norm functional subject to an elliptic PDE and state constraints

## Title data

Prüfert, Uwe ; Schiela, Anton:
The minimization of a maximum-norm functional subject to an elliptic PDE and state constraints.
In: ZAMM : Zeitschrift für angewandte Mathematik und Mechanik. Vol. 89 (2009) Issue 7 . - pp. 536-551.
ISSN 1521-4001
DOI: https://doi.org/10.1002/zamm.200800097

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## Project information

Project title:
Project's official titleProject's id
DFG Research Center Matheon "Mathematics for key technologies"FZT 86

Project financing: Deutsche Forschungsgemeinschaft

## Abstract in another language

We study the optimal control of a maximum-norm objective functional subjected to an elliptic-type PDE and pointwise state constraints. The problem is transformed into a problem where the non-differentiable maximum-norm in the functional will be replaced by a scalar variable and additional state constraints. This problem is solved by barrier methods. We will show the existence and convergence of the central path for a class of barrier functions. Numerical experiments complete the presentation.

## Further data

Item Type: Article in a journal Yes A preliminary version is published under the title "The minimization of an L^∞-functional [$L^{\infty}$-functional] subject to an elliptic PDE and state constraints" at the Konrad-Zuse-Zentrum für Informationstechnik, Berlin as ZIB-Report 08-17. optimal control; maximum-norm functional; state constrained optimization; barrier methods Mathematics Subject Classification Code: 49K20 (65K05 90C25) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics) > Professorship Applied Mathematics (Applied Mathematics) - Univ.-Prof. Dr. Anton SchielaProfile Fields > Advanced Fields > Nonlinear DynamicsFacultiesFaculties > Faculty of Mathematics, Physics und Computer ScienceFaculties > Faculty of Mathematics, Physics und Computer Science > Department of MathematicsFaculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics)Profile FieldsProfile Fields > Advanced Fields No 500 Science > 510 Mathematics 17 Mar 2015 09:58 10 Mar 2016 10:59 https://eref.uni-bayreuth.de/id/eprint/8081