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Type of Publication:  Diploma thesis 
URI (citable link):  http://nbnresolving.de/urn:nbn:de:bsz:3520255879 
Author:  Rogg, Sabrina 
Year of publication:  2014 
Summary: 
In this diploma thesis an optimal control problem governed by a semilinear heat equation is considered. The problem is formulated as a reduced problem by including the semilinear heat equation in the formulation of the cost functional. This nonlinear reduced problem is numerically solved by a globalized inexact Newton method. The inexact Newton steps are computed with a conjugate gradient (CG) algorithm. In a first approach, an Armijo backtracking strategy is chosen for globalization of the NewtonCG method. A classical Finite Element Galerkin technique is used for spatial discretization. To reduce the computational effort a model reduction approach based on proper orthogonal decomposition (POD) is applied. A control which is utilized to set up the POD basis has to be chosen at the beginning and the reducedorder models (ROMs) are fixed during optimization. If the required control is chosen badly, few POD basis functions do not suffice to obtain good POD suboptimal controls. To overcome this problem the reducedorder NewtonCG strategy is embedded in a trust region framework, where the POD basis and hence the ROMs are improved successively by utilizing the updated control values. The proposed methods are tested by numerical examples. In particular, the adaptation of the POD basis when applying the trust region POD strategy is analyzed.

Dissertation note:  Master thesis, Universität Konstanz 
Subject (DDC):  510 Mathematics 
Keywords:  Optimal control, semilinear partial differential equations, globalized inexact Newton methods, model reduction, proper orthogonal decomposition, trust region methods 
Comment on publication:  Diplomarbeit 
Link to License:  In Copyright 
Bibliography of Konstanz:  Yes 
ROGG, Sabrina, 2014. Trust Region POD for Optimal Boundary Control of a Semilinear Heat Equation [Master thesis]. Konstanz: Universität Konstanz
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