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On Optimality Conditions in Control of Elliptic Variational Inequalities
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SYSNO ASEP 0356042 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On Optimality Conditions in Control of Elliptic Variational Inequalities Author(s) Outrata, Jiří (UTIA-B) RID, ORCID
Jarušek, Jiří (MU-W) RID, ORCID, SAI
Stará, J. (CZ)Source Title Set-Valued and Variational Analysis. - : Springer - ISSN 1877-0533
Roč. 19, č. 1 (2011), s. 23-42Number of pages 20 s. Language eng - English Country NL - Netherlands Keywords Directional differentiability ; Critical cone ; Strong local fuzzy sum rule ; Calmness ; Capacity Subject RIV BA - General Mathematics R&D Projects IAA100750802 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) GA201/09/0917 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10750506 - UTIA-B (2005-2011) AV0Z10190503 - MU-W (2005-2011) UT WOS 000286832900002 DOI 10.1007/s11228-010-0158-4 Annotation In the paper we consider optimal control of a class of strongly monotone variational inequalities, whose solution map is directionally differentiable in the control variable. This property is used to derive sharp pointwise necessary optimality conditions provided we do not impose any control or state constraints. In presence of such constraints we make use of the generalized differential calculus and derive, under a mild constraint qualification, optimality conditions in a “fuzzy” form. For strings, these conditions may serve as an intermediate step toward pointwise conditions of limiting (Mordukhovich) type and in the case of membranes they lead to a variant of Clarke stationarity conditions. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2011
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