Results 201 to 210 of about 139,538 (244)

Generalized Lipschitz Functions

Computational Methods and Function Theory, 2006
Lipschitz classes with variable exponents \(\text{Lip}_{\alpha(t)}\) are introduced. The exponents \({\alpha(t)}\) (called test functions) are supposed to be real-valued continuous functions defined in the right neighbourhood of zero satisfying the following conditions: \[ 1)\;{\alpha(t) = \alpha + o(1)},\;\alpha\in {\mathbb R};\quad 2) \;\int_{0}^{t} \
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Locally Lipschitz Functionals

2021
In this chapter we focus our attention on the theory developed by Clarke for locally Lipschitz functionals. More precisely, we will investigate the properties of the generalized directional derivative and the Clarke subdifferential as well as the connection with the convex subdifferential.
Nicuşor Costea   +2 more
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MAKING CONTINUOUS FUNCTIONS LIPSCHITZ

Rocky Mountain Journal of Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Artstein, Zvi, Beer, Gerald
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Generalized Lipschitz functions

Nonlinear Analysis: Theory, Methods & Applications, 2000
The aim of the reviewing article is to extend the concept of Lipschitz functions in such a way that it include nondecreasing functions and functions with bounded (below) derivatives. Jouini introduces such a general concept and proves that every bounded subset of generalized Lipschitz functions is relatively compact. More precisely, let \(Q\) be a cone
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Smoothing Lipschitz functions

Optimization Methods and Software, 2007
This paper describes a new approach to multivariate scattered data smoothing. It is assumed that the data are generated by a Lipschitz continuous function f, and include random noise to be filtered out. The proposed approach uses known, or estimated value of the Lipschitz constant of f, and forces the data to be consistent with the Lipschitz properties
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Lipschitz Functions and Ekeland’s Theorem

Journal of Optimization Theory and Applications, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Beer, Gerald, Ceniceros, Jose
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Stochastic Lipschitz functions

Cybernetics, 1986
We study the subdifferential of \textit{F. H. Clarke} [Trans. Amer. Math. Soc. 205, 247-262 (1975; Zbl 0307.26012)] or random Lipschitz functions. We show that it is a multivalued mapping which is measurable in the collection of determinate and stochastic variables.
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Learning lipschitz functions

International Journal of Computer Mathematics, 1995
Considered here is the problem of learning a nonlinear mapping with uncountable domain and range. The learning model used is that of piecewise linear interpolation on random samples from the domain. More specifically, a network learns a function by approximating its value, typically within some small ∈, when presented an arbitrary element of the domain.
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Lipschitz pre-orders and Lipschitz utility functions

Russian Mathematical Surveys, 1984
The notion of the Lipschitz preorder as a preference ordering relation on a separable metric space is introduced, and it is shown that it leads to a Lipschitz utility function.
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