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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
Refereed: Yes
Additional notes: 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.
Keywords: optimal control; maximum-norm functional; state constrained optimization; barrier methods
Subject classification: Mathematics Subject Classification Code: 49K20 (65K05 90C25)
Institutions of the University: 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 Schiela
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 17 Mar 2015 09:58
Last Modified: 10 Mar 2016 10:59
URI: https://eref.uni-bayreuth.de/id/eprint/8081