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A Composite Step Method with Inexact Step Computations for PDE Constrained Optimization

Title data

Schaller, Manuel ; Schiela, Anton ; Stöcklein, Matthias:
A Composite Step Method with Inexact Step Computations for PDE Constrained Optimization.
Bayreuth , 2018 . - 29 p.

Official URL: Volltext

Project information

Project title:
Project's official titleProject's id
Specialized Adaptive Algorithms for Model Predictive Control of PDEsGR 1569/17-1
Specialized Adaptive Algorithms for Model Predictive Control of PDEsSCHI 1379/5-1
Optimal Control of Static Contact in Finite Strain ElasticitySCHI 1379/2-1

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

We consider a composite step algorithm for equality constrained optimization problems. The arising linear systems are inexactly solved with a conjugate gradient method using a constraint preconditioner. The influence of the error on the damping parameters of the underlying Newton scheme and algorithmic parameters is discussed and specialized termination criteria for the conjugate gradient method are given. Application to optimal control of a quasilinear heat equation and nonlinear elasticity illustrates the numerical performance of the resulting algorithm.

Further data

Item Type: Preprint, postprint, working paper, discussion paper
Additional notes: Preprint Number SPP1962-098
Keywords: optimization with PDEs; cubic regularization; affine covariance; composite step methods; nonlinear elasticity
Subject classification: Mathematics Subject Classification Code: 49M37, 90C55, 90C06
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 > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne)
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 > 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 > Chair Applied Mathematics (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 05 Nov 2018 07:42
Last Modified: 14 Mar 2019 14:18
URI: https://eref.uni-bayreuth.de/id/eprint/46227