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

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 rel...

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Bibliographic Details
Published in:Nonlinear analysis Vol. 71; no. 3; pp. 1213 - 1226
Main Authors: Henrion, R., Outrata, J., Surowiec, T.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Ltd 01.08.2009
Elsevier
Subjects:
Calmness
Exact sciences and technology
Inequality constraints
Mathematical analysis
Mathematics
Mordukhovich coderivative
Normal cone mapping
Sciences and techniques of general use
Mordukhovich coderivative
90C30
49J53
Calmness
Inequality constraints
Normal cone mapping
Nonlinear analysis
Inequality constraint
Mathematical model
ISSN:0362-546X, 1873-5215
Online Access:Get full text
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Summary: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.
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ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2008.11.089