About: On the co-derivative of normal cone mappings to inequality systems

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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. 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. (en)
Title	On the co-derivative of normal cone mappings to inequality systems On the co-derivative of normal cone mappings to inequality systems (en)
skos:prefLabel	On the co-derivative of normal cone mappings to inequality systems On the co-derivative of normal cone mappings to inequality systems (en)
skos:notation	RIV/67985556:_____/09:00326339!RIV10-AV0-67985556
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA1030405), Z(AV0Z10750506)
http://linked.open...iv/cisloPeriodika	3-4
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Outrata, Jiří
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	331490
http://linked.open...ai/riv/idVysledku	RIV/67985556:_____/09:00326339
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Mordukhovich coderivative; Normal cone mapping; Calmness; Inequality constraints (en)
http://linked.open.../riv/klicoveSlovo	Mordukhovich coderivative Normal cone mapping Inequality constraints Calmness
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[D8DC0E2D6B6A]
http://linked.open...i/riv/nazevZdroje	Nonlinear Analysis: Theory, Methods & Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Development of software system for solving large-scale problems of nonlinear and nonsmooth optimization
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	71
http://linked.open...iv/tvurceVysledku	Outrata, Jiří Henrion, R. Surowiec, T.
http://linked.open...ain/vavai/riv/wos	000266699600051
http://linked.open...n/vavai/riv/zamer	Pokročilé matematické metody získávání, zpracování a využití informací a znalostí ve složitých a nedeterministických systémech
issn	0362-546X
number of pages	14 (xsd:int)
is http://linked.open...avai/riv/vysledek of	On the co-derivative of normal cone mappings to inequality systems On the co-derivative of normal cone mappings to inequality systems On the co-derivative of normal cone mappings to inequality systems On the co-derivative of normal cone mappings to inequality systems

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