On New Generalized Differentials with Respect to a Set and Their Applications
The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a set of multifunctions and singleton mappings, respectively, b...
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| Veröffentlicht in: | Set-valued and variational analysis Jg. 32; H. 3; S. 27 |
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| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
01.09.2024
Springer Nature B.V |
| Schlagworte: | |
| ISSN: | 1877-0533, 1877-0541 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a set of multifunctions and singleton mappings, respectively, based on these normal cones. The necessary and sufficient conditions for the Aubin property with respect to a set of multifunctions are then described by using the limiting coderivative with respect to a set. As a result of the limiting subdifferential with respect to a set, we offer the requisite optimality criteria for local solutions to optimization problems. In addition, we also provide examples to demonstrate the outcomes. |
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| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1877-0533 1877-0541 |
| DOI: | 10.1007/s11228-024-00729-z |