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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Bibliographic Details
Published in:Set-valued and variational analysis Vol. 19; no. 4; pp. 505 - 536
Main Authors: Li, Shengjie, Penot, Jean-Paul, Xue, Xiaowei
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.12.2011
Subjects:
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
Online Access:Get full text
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Summary: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