Attainment and (sub)differentiability of the supremal convolution of a function and square of the norm

DOI10.1016/j.jmaa.2012.03.052zbMath1252.46073OpenAlexW4206687731MaRDI QIDQ432421

Martin Fabian, Radek Cibulka

Publication date: 4 July 2012

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.03.052

zbMATH Keywords

subdifferentialdense \(G_\delta\) setdensely remotal setfarthest distance functionFréchet and Gâteaux differentiabilitylocally uniformly rotund normstrong attainmentsupremal convolution

Mathematics Subject Classification ID

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Derivatives of functions in infinite-dimensional spaces (46G05) Real-valued functions on manifolds (58C05)

Related Items

The NSLUC property and Klee envelope ⋮ The attainment set of the $\varphi$-envelope and genericity properties

Cites Work

• Convex functions, monotone operators and differentiability.
• Differentiability of Lipschitz functions on Banach spaces
• On Chebyshev functions and Klee functions
• Attainment and (sub)differentiability of the infimal convolution of a function and the square of the norm
• Banach space theory. The basis for linear and nonlinear analysis
• Differentiation of Real-Valued Functions and Continuity of Metric Projections
• Metric projections and the differentiability of distance functions
• Farthest points and the farthest distance map
• Generalized subdifferential of the distance function