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Title
Obstacle Problems with Cohesion: A Hemi-Varitional Inequality approach and its efficient numerical solution
AuthorHintermüller, Michael In der Gemeinsamen Normdatei der DNB nachschlagen ; Kovtunenko, Victor A. ; Kunisch, Karl In der Gemeinsamen Normdatei der DNB nachschlagen
Published in
SIAM journal on control and optimization / Society for Industrial and Applied Mathematics, Philadelphia, Pa. : Soc., 1.1962 -, Vol. 21, Issue 2, page 491-516
PublishedSIAM
LanguageEnglish
Document typeJournal Article
Keywords (EN)obstacle problem with cohesion / generalized complementarity problem / hemivariational inequality / nonsmooth optimization / primal-dual active set algorithm / generalized Newton method
ISSN1095-7138
URNurn:nbn:at:at-ubg:3-458 Persistent Identifier (URN)
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 The work is publicly available
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Obstacle Problems with Cohesion: A Hemi-Varitional Inequality approach and its efficient numerical solution [1.23 mb]
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Abstract (English)

Motivated by an obstacle problem for a membrane subject to cohesion forces, constrained minimization problems involving a nonconvex and nondifferentiable objective functional representing the total potential energy are considered. The associated first-order optimality system leads to a hemivariational inequality, which can also be interpreted as a special complementarity problem in function space. Besides an analytical investigation of first-order optimality, a primal-dual active set solver is introduced. It is associated to a limit case of a semismooth Newton method for a regularized version of the underlying problem class. For the numerical algorithms studied in this paper, global as well as local convergence properties are derived and verified numerically.

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