Guaranteed Upper Bounds for Iteration Errors and Modified Kačanov Schemes via Discrete Duality

We apply duality theory to discretized convex minimization problems to obtain computable guaranteed upper bounds for the distance of given discrete functions and the exact discrete minimizer. Furthermore, we show that the discrete duality framework extends convergence results for the Kačanov scheme...

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Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 25; no. 3; pp. 587 - 600
Main Authors Diening, Lars, Storn, Johannes
Format Journal Article
LanguageEnglish
Published Minsk De Gruyter 01.07.2025
Walter de Gruyter GmbH
Subjects
35J70
49M29
65N22
65N30
Computational Calculus of Variations
Discrete Duality
Discrete functions
Iteration Error
Kačanov Scheme
Upper bounds
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Summary:We apply duality theory to discretized convex minimization problems to obtain computable guaranteed upper bounds for the distance of given discrete functions and the exact discrete minimizer. Furthermore, we show that the discrete duality framework extends convergence results for the Kačanov scheme to a broader class of problems.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2025-0017