On Fréchet differentiability of multifunctions

DOI10.1080/02331930500100148zbMath1095.49017OpenAlexW2044764017MaRDI QIDQ5317735

Valentin V. Gorokhovik, Peter P. Zabreĭko

Publication date: 21 September 2005

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: http://elib.bsu.by/handle/123456789/12812

zbMATH Keywords

Fréchet differentiabilitymultifunctionHausdorff metricaffine multifunctiondifference-sublinear mappings

Mathematics Subject Classification ID

Set-valued and variational analysis (49J53) Fréchet and Gateaux differentiability in optimization (49J50) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Set-valued and function-space-valued mappings on manifolds (58C06)

Related Items (8)

\((\Lambda ,C)\)-contingent derivatives of set-valued maps ⋮ About Hahn-Banach extension theorems and applications to set-valued optimization ⋮ An extension of the Carathéodory differentiability to set-valued maps ⋮ \(\tau ^w\)-contingent epiderivatives in reflexive spaces ⋮ Representations of affine multifunctions by affine selections ⋮ Decomposition of Minkowski-Rådström-Hörmander space to the direct sum of symmetric and asymmetric subspaces ⋮ Completeness in Minkowski–Rådström–Hörmander spaces ⋮ A characterization of cone-convexity for set-valued functions by cone-quasiconvexity

Cites Work

• Approximation to a set-valued mapping. I: A proposal
• Generalized differential calculus for nonsmooth and set-valued mappings
• On set-valued differentiation and integration
• A calculus for set-valued maps and set-valued evolution equations
• A differential calculus for multifunctions
• Nonconvex differential calculus for infinite-dimensional multifunctions
• Adjoint Process Duality
• Differentiability of Relations and Differential Stability of Perturbed Optimization Problems
• The eclipsing concept to approximate a multi-valued mapping
• Affine and eclipsing multifunctions
• coderivatives of set-valued mappings: Calculus and applications
• Differentiability of Set-Valued Maps in Banach Spaces
• Differentiability and regularity of Lipschitzian mappings

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