Kolmogorov entropy for classes of convex functions

DOI10.1007/s00365-009-9053-3zbMath1177.41022OpenAlexW1963490725MaRDI QIDQ836088

Dimiter P. Dryanov

Publication date: 31 August 2009

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-009-9053-3

zbMATH Keywords

asymptotic behaviorconvex functionHamming distanceKolmogorov \(\varepsilon\)-entropy\(L_p\) metricmassivity of a set

Mathematics Subject Classification ID

Convex functions and convex programs in convex geometry (52A41) Entropy in general topology (54C70) Convex sets in (2) dimensions (including convex curves) (52A10) Duality and reflexivity in normed linear and Banach spaces (46B10) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (9)

Global rates of convergence of the MLEs of log-concave and \(s\)-concave densities ⋮ An improved global risk bound in concave regression ⋮ Bracketing numbers of convex and \(m\)-monotone functions on polytopes ⋮ Entropy of convex functions on \(\mathbb R^d\) ⋮ Covering numbers for bounded variation functions ⋮ Covering numbers of \(L_{p}\)-balls of convex functions and sets ⋮ Metric Entropy for Functions of Bounded Total Generalized Variation ⋮ Global risk bounds and adaptation in univariate convex regression ⋮ Sharp estimates for the covering numbers of the Weierstrass fractal kernel

Cites Work

• Universal Donsker classes and metric entropy
• A survey of the theory of hypercube graphs
• An inequality for trigonometric polynomials and its application for estimating the entropy numbers
• Metric entropy of some classes of sets with differentiable boundaries
• Metric Entropy of Convex Hulls in Hilbert Spaces
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