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An affine covariant composite step method for optimization with PDEs as equality constraints

URN to cite this document: urn:nbn:de:0297-zib-53954

Title data

Lubkoll, Lars ; Schiela, Anton ; Weiser, Martin:
An affine covariant composite step method for optimization with PDEs as equality constraints.
Konrad-Zuse-Zentrum für Informationstechnik Berlin
Berlin, Germany , 2015 . - 40 S. - (ZIB-Report ; 15-09 )

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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

We propose a composite step method, designed for equality constrained optimization with partial differential equations. Focus is laid on the construction of a globalization scheme, which is based on cubic regularization of the objective and an affine covariant damped Newton method for feasibility. We show finite termination of the inner loop and fast local convergence of the algorithm. We discuss preconditioning strategies for the iterative solution of the arising linear systems with projected conjugate gradient. Numerical results are shown for optimal control problems subject to a nonlinear heat equation and subject to nonlinear elastic equations arising from an implant design problem in craniofacial surgery.

Further data

Item Type: Preprint, postprint
Keywords: composite step methods; cubic regularization; affine covariant; optimization with PDEs
Subject classification: Mathematics Subject Classification Code: 49M37 (90C55 90C06)
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: 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 > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics (Applied Mathematics) > Chair Applied Mathematics (Applied Mathematics) - Univ.-Prof. Dr. Anton Schiela
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics (Applied Mathematics)
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:0297-zib-53954
Date Deposited: 02 Jun 2015 06:19
Last Modified: 21 Mar 2019 10:43
URI: https://epub.uni-bayreuth.de/id/eprint/1930

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