On the co-derivative of normal cone mappings to inequality systems
Please always quote using this URN:urn:nbn:de:0296-matheon-5325
- 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.
Author: | Rene Henrion, Jiri Outrata, Thomas Surowiec |
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URN: | urn:nbn:de:0296-matheon-5325 |
Referee: | Fredi Tröltzsch |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2008/11/11 |
Release Date: | 2008/10/11 |
Tag: | |
Institute: | Humboldt-Universität zu Berlin |
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) | |
MSC-Classification: | 49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J53 Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06] |
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C30 Nonlinear programming | |
Preprint Number: | 528 |