Differentiability of cone-monotone functions on separable Banach space

DOI10.1090/S0002-9939-03-07149-1zbMath1042.49016MaRDI QIDQ4452196

Jonathan M. Borwein, James V. Burke, Adrian S. Lewis

Publication date: 12 February 2004

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

monotonicitylower semicontinuityconvex coneGâteaux differentiabilityHadamard derivativenull setsdirectionally Lipschitz functions

Mathematics Subject Classification ID

Fréchet and Gateaux differentiability in optimization (49J50) Derivatives of functions in infinite-dimensional spaces (46G05)

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Haar null and Haar meager sets: a survey and new results ⋮ Gâteaux differentiability of cone-monotone and pointwise Lipschitz functions ⋮ Cone monotone mappings: continuity and differentiability ⋮ Convex sub-differential sum rule via convex semi-closed functions with applications in convex programming ⋮ On properties of different notions of centers for convex cones ⋮ Monotonic grey box direct search optimization ⋮ Unnamed Item ⋮ Convergence of the gradient sampling algorithm on directionally Lipschitz functions ⋮ On the nondifferentiability of cone-monotone functions in Banach spaces ⋮ Clarke Subgradients for Directionally Lipschitzian Stratifiable Functions ⋮ Differentiability of quasiconvex functions on separable Banach spaces

Cites Work

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• Cone-Monotone Functions: Differentiability and Continuity
• On the nondifferentiability of cone-monotone functions in Banach spaces
• Continuity and differentiability properties of monotone real functions of several real variables
• Variational Analysis
• Null Sets and Essentially Smooth Lipschitz Functions
• Approximating Subdifferentials by Random Sampling of Gradients

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