An extension theorem for convex functions of class \(C^{1,1}\) on Hilbert spaces

DOI10.1016/j.jmaa.2016.09.015zbMath1364.26017arXiv1603.00241OpenAlexW2963797349MaRDI QIDQ333855

Carlos Mudarra, Daniel Azagra

Publication date: 31 October 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.00241

zbMATH Keywords

convex functiondifferentiable mappingWhitney extension theoremLipschitz condition\(C^{1,1}\) functionextension of functions

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Extension of maps (54C20) (C^infty)-functions, quasi-analytic functions (26E10) Convexity of real functions of several variables, generalizations (26B25) Continuous and differentiable maps in nonlinear functional analysis (46T20) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (6)

Explicit formulas for 𝐶^{1,1} Glaeser-Whitney extensions of 1-Taylor fields in Hilbert spaces ⋮ On the Properties of Convex Functions over Open Sets ⋮ Worst-Case Convergence Analysis of Inexact Gradient and Newton Methods Through Semidefinite Programming Performance Estimation ⋮ Explicit formulas for \(C^{1,1}\) and \(C_{\operatorname{conv}}^{1, \omega}\) extensions of 1-jets in Hilbert and superreflexive spaces ⋮ Prescribing tangent hyperplanes to $C^{1,1}$ and $C^{1,\omega}$ convex hypersurfaces in Hilbert and superreflexive Banach spaces ⋮ On the oracle complexity of smooth strongly convex minimization

Cites Work

• Unnamed Item
• Étude de quelques algèbres tayloriennes
• Differentiable functions on Banach spaces with Lipschitz derivatives
• On smooth extensions of vector-valued functions defined on closed subsets of Banach spaces
• Minimal Lipschitz extensions to differentiable functions defined on a Hilbert space

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