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ALGORITHMIC ASPECTS OF LIPSCHITZ FUNCTIONS
"... Abstract. We characterize the variation functions of computable Lipschitz functions. We show that a real z is computably random if and only if every computable Lipschitz function is differentiable at z. Furthermore, a real z is Schnorr random if and only if every Lipschitz function with L1-computabl ..."
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Cited by 9 (4 self)
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Abstract. We characterize the variation functions of computable Lipschitz functions. We show that a real z is computably random if and only if every computable Lipschitz function is differentiable at z. Furthermore, a real z is Schnorr random if and only if every Lipschitz function with L1
BANDLIMITED LIPSCHITZ FUNCTIONS
"... Abstract. We study the space of bandlimited Lipschitz functions in one variable. In particular we provide a geometrical description of interpolating and sampling sequences for this space. We also give a description of the trace of such functions to sequences of critical density in terms of a cancell ..."
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Abstract. We study the space of bandlimited Lipschitz functions in one variable. In particular we provide a geometrical description of interpolating and sampling sequences for this space. We also give a description of the trace of such functions to sequences of critical density in terms of a
A rough Lipschitz Function
, 2002
"... A famous theorem of H. Lebesgue states that a Lipschitz function f: [0, 1] → R is differentiable at almost every point. Approximation by linear functions at the scale r is measured by βf(x, r) = inf a,b∈R ..."
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A famous theorem of H. Lebesgue states that a Lipschitz function f: [0, 1] → R is differentiable at almost every point. Approximation by linear functions at the scale r is measured by βf(x, r) = inf a,b∈R
Directional Derivatives Of Lipschitz Functions
, 2000
"... Let f be a Lipschitz mapping of a separable Banach space X to a Banach space Y . We observe that the set of points at which f is differentiable in a spanning set of directions but not Gateaux differentiable is oe-directionally porous. Since Borel oe- directionally porous sets, in addition to bei ..."
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Cited by 19 (2 self)
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Let f be a Lipschitz mapping of a separable Banach space X to a Banach space Y . We observe that the set of points at which f is differentiable in a spanning set of directions but not Gateaux differentiable is oe-directionally porous. Since Borel oe- directionally porous sets, in addition
Distance-based classification with lipschitz functions
- Journal of Machine Learning Research
, 2003
"... The goal of this article is to develop a framework for large margin classification in metric spaces. We want to find a generalization of linear decision functions for metric spaces and define a corresponding notion of margin such that the decision function separates the training points with a large ..."
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Cited by 30 (2 self)
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margin. It will turn out that using Lipschitz functions as decision functions, the inverse of the Lipschitz constant can be interpreted as the size of a margin. In order to construct a clean mathematical setup we isometrically embed the given metric space into a Banach space and the space of Lipschitz
Essentially Strictly Differentiable Lipschitz Functions
- J. FUNCTIONAL ANALYSIS
, 1995
"... In this paper we address some of the most fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on Banach spaces. For example, we examine the relationship between integrability, D-representability and strict differentiability. In addition to this, we ..."
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Cited by 6 (4 self)
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In this paper we address some of the most fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on Banach spaces. For example, we examine the relationship between integrability, D-representability and strict differentiability. In addition to this, we
Parametric Optimization for the Lipschitz Function
"... We consider the parametric minimization problem with a Lipschitz objective function. We propose an approach for solving the original problem in a finite number of steps in order to obtain a solution with a given accuraly. ..."
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We consider the parametric minimization problem with a Lipschitz objective function. We propose an approach for solving the original problem in a finite number of steps in order to obtain a solution with a given accuraly.
NONLINEAR ISOMORPHISMS OF LATTICES OF LIPSCHITZ FUNCTIONS
"... Abstract. The paper contains a number of Banach–Stone type theorems for lattices of uniformly continuous and Lipschitz functions without any linearity assumption. Sample result: two complete metric spaces of finite diameter are Lipschitz homeomorphic if (and only if, of course) the corresponding lat ..."
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Cited by 1 (0 self)
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Abstract. The paper contains a number of Banach–Stone type theorems for lattices of uniformly continuous and Lipschitz functions without any linearity assumption. Sample result: two complete metric spaces of finite diameter are Lipschitz homeomorphic if (and only if, of course) the corresponding
Results 1 - 10
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