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An interior point algorithm with inexact step computation in function space for state constrained optimal control

Title data

Schiela, Anton ; Günther, Andreas:
An interior point algorithm with inexact step computation in function space for state constrained optimal control.
In: Numerische Mathematik. Vol. 119 (2011) Issue 2 . - pp. 373-407.
ISSN 0029-599X
DOI: https://doi.org/10.1007/s00211-011-0381-4

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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 consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is controlled by adaptive grid refinement in the innermost loop. This allows to perform most of the required Newton steps on coarse grids, such that the overall computational time is dominated by the last few steps. For this purpose we propose an a-posteriori error
estimator for a problem suited norm.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: A preliminary version under the title "Interior Point Methods in Function Space for State Constraints - Inexact Newton and Adaptivity" is published at the Konrad-Zuse-Zentrum für Informationstechnik, Berlin as ZIB-Report 09-01.
Keywords: adaptivity; function space; interior point methods; state constraints
Subject classification: Mathematics Subject Classification Code: 90C51 (49M05)
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 09:08
Last Modified: 17 Mar 2015 09:08
URI: https://eref.uni-bayreuth.de/id/eprint/8049