Characterizing Generalized Derivatives of Set-Valued Maps: Extending the Tangential and Normal Approaches
For a set-valued map, we characterize, in terms of its (unconvexified or convexified) graphical derivatives near the point of interest, positively homogeneous maps that are generalized derivatives in the sense of [C. H. J. Pang, Math. Oper. Res., 36 (2011), pp. 377--397]. This result generalizes the...
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| Veröffentlicht in: | SIAM journal on control and optimization Jg. 51; H. 1; S. 145 - 171 |
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| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.2013
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| Schlagworte: | |
| ISSN: | 0363-0129, 1095-7138 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | For a set-valued map, we characterize, in terms of its (unconvexified or convexified) graphical derivatives near the point of interest, positively homogeneous maps that are generalized derivatives in the sense of [C. H. J. Pang, Math. Oper. Res., 36 (2011), pp. 377--397]. This result generalizes the Aubin criterion in [A. L. Dontchev, M. Quincampoix, and N. Zlateva, J. Convex Anal., 3 (2006), pp. 45--63]. A second characterization of these generalized derivatives is easier to check in practice, especially in the finite dimensional case. Finally, the third characterization in terms of limiting normal cones and coderivatives generalizes the Mordukhovich criterion in the finite dimensional case. The convexified coderivative has a bijective relationship with the set of possible generalized derivatives. We conclude by illustrating a few applications of our result. [PUBLICATION ABSTRACT] |
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| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23 |
| ISSN: | 0363-0129 1095-7138 |
| DOI: | 10.1137/110840467 |