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On the co-derivative of normal cone mappings to inequality systems
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SYSNO ASEP 0326339 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On the co-derivative of normal cone mappings to inequality systems Title O koderiva normalově-kuželového zobrazení k systémům nerovnic Author(s) Henrion, R. (DE)
Outrata, Jiří (UTIA-B) RID, ORCID
Surowiec, T. (DE)Source Title Nonlinear Analysis: Theory, Methods & Applications. - : Elsevier - ISSN 0362-546X
Roč. 71, 3-4 (2009), s. 1213-1226Number of pages 14 s. Publication form www - www Language eng - English Country GB - United Kingdom Keywords Mordukhovich coderivative ; Normal cone mapping ; Calmness ; Inequality constraints Subject RIV BA - General Mathematics R&D Projects IAA1030405 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10750506 - UTIA-B (2005-2011) UT WOS 000266699600051 DOI 10.1016/j.na.2008.11.089 Annotation The paper deals with co-derivative formulae for normal cone mappings to smooth inequality systems. Both the regular (Linear Independence Constraint Qualification satisfied) and nonregular (Mangasarian-Fromovitz Constraint Qualification satisfied) cases are considered. A major part of the results relies on general transformation formulae previously obtained by Mordukhovich and Outrata. This allows one to derive exact formulae for general smooth, regular and polyhedral, possibly nonregular systems. In the nonregular, nonpolyhedral case a generalized transformation formula by Mordukhovich and Outrata applies, however, a major difficulty consists in checking a calmness condition of a certain multivalued mapping. The paper provides a translation of this condition in terms of much easier to verify constraint qualifications. The final section is devoted to the situation where the calmness condition is violated. A series of examples illustrates the use and comparison of the presented formulae. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2010
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