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Title
Optimal shape design subject to elliptic variational inequalities
AuthorHintermüller, Michael In der Gemeinsamen Normdatei der DNB nachschlagen ; Laurain, Antoine
Published in
SIAM Journal Control and Optimization, Philadelphia, Pa., 2011, Vol. 49, Issue 3, page 1015-1047
PublishedSIAM
Edition
Publisher version
LanguageEnglish
Document typeJournal Article
Keywords (EN)asymptotic analysis / elliptic variational inequality / free boundary problem / level set method / obstacle problem / shape and topology optimization
URNurn:nbn:at:at-ubg:3-726 Persistent Identifier (URN)
DOIdoi:10.1137/080745134 
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 The work is publicly available
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Abstract (English)

A mathematical framework for optimal bilinear control of nonlinear Schrödingerequations of GrossPitaevskii type arising in the description of BoseEinstein condensates is presented.The obtained results generalize earlier efforts found in the literature in several aspects. Inparticular, the cost induced by the physical workload over the control process is taken into accountrather than the often used L2- or H1-norms for the cost of the control action. Well-posedness ofthe problem and existence of an optimal control are proved. In addition, the first order optimalitysystem is rigorously derived. Also a numerical solution method is proposed, which is based on aNewton-type iteration, and used to solve several coherent quantum control problems.

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