Codifferential Calculus

In this paper, some exact calculus rules are obtained for calculating the coderivatives of the composition of two multivalued maps. Similar rules are displayed for sums. A crucial role is played by an intermediate set-valued map called the resolvent. We first establish inclusions for contingent, Fré...

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Vydané v:Set-valued and variational analysis Ročník 19; číslo 4; s. 505 - 536
Hlavní autori: Li, Shengjie, Penot, Jean-Paul, Xue, Xiaowei
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Dordrecht Springer Netherlands 01.12.2011
Predmet:
Analysis
Mathematics
Mathematics and Statistics
Optimization
Allied sets
Lower semicontinuity
54B20
Normal cone
Coderivative
Synergetic sets
Openness with a linear rate
54C60
47H04
ISSN:1877-0533, 1877-0541
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Shrnutí:In this paper, some exact calculus rules are obtained for calculating the coderivatives of the composition of two multivalued maps. Similar rules are displayed for sums. A crucial role is played by an intermediate set-valued map called the resolvent. We first establish inclusions for contingent, Fréchet and limiting coderivatives. Combining them, we get equality rules. The qualification conditions we present are natural and less exacting than classical conditions.
ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-010-0171-7