Helping you finding an appropriate regularization process
type: Item
instance of: scholarly article
title: Helping you finding an appropriate regularization process
zbMATH Open document ID: 1393.49011
author: Huynh Van Ngai
author: Jean-Paul Penot
published in: Vietnam Journal of Mathematics
publication date: 2018-06-13T00:00:00Z
review text: The authors survey different approaches related to the regularization of a nonsmooth function. The infimal convolution regularization, which generalizes the Moreau envelope to Banach spaces and to the setting of nonconvex functions, is studied in detail.
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 46N10
Mathematics Subject Classification ID: 46T20
zbMATH DE Number: 6888005
zbMATH Keywords: compensated convexity
zbMATH Keywords: convolution
zbMATH Keywords: differentiability
zbMATH Keywords: infimal convolution
zbMATH Keywords: nonsmooth analysis
zbMATH Keywords: regularization
zbMATH Keywords: subdifferential
reviewed by: Radu I. Boţ
MaRDI profile type: Publication
full work available at URL: s10013-018-0293-z
OpenAlex ID: W2801192337
cites work: Q5441008
cites work: Fréchet differentiability of convex functions
cites work: Q5186236
cites work: Approximation and regularization of arbitrary functions in Hilbert spaces by the Lasry-Lions method
cites work: Set-valued analysis
cites work: Q3057940
cites work: Q3952640
cites work: Smoothing and first order methods: a unified framework
cites work: Q4022327
cites work: Approximation and regularisation of arbitrary sets in finite dimension
cites work: Q4938152
cites work: Prox-regular functions in Hilbert spaces
cites work: Uniform prox-regularity of functions and epigraphs in Hilbert spaces
cites work: Q3422488
cites work: Prox-regular sets and epigraphs in uniformly convex Banach spaces: Various regularities and other properties
cites work: Integration of primal lower nice functions in Hilbert spaces
cites work: The Proximal Normal Formula in Banach Space
cites work: Techniques of variational analysis
cites work: Towards minimal assumptions for the infimal convolution regularization
cites work: Functional analysis, Sobolev spaces and partial differential equations
cites work: Epi-convergent smoothing with applications to convex composite functions
cites work: ENVELOPES FOR SETS AND FUNCTIONS: REGULARIZATION AND GENERALIZED CONJUGACY
cites work: Semiconcave functions, Hamilton-Jacobi equations, and optimal control
cites work: Approximation of Lipschitz functions by \(\Delta\)-convex functions in Banach spaces
cites work: On regularization in superreflexive Banach spaces by infimal convolution formulas
cites work: Functional Analysis, Calculus of Variations and Optimal Control
cites work: Q2995188
cites work: Q3917070
cites work: Geometry of Banach spaces. Selected topics
cites work: Q3200121
cites work: Smooth approximations
cites work: Euler-Lagrange and Hamiltonian formalisms in dynamic optimization
cites work: Q4817577
cites work: Differential properties of the Moreau envelope
cites work: Subdifferential characterization ofs-lower regular functions
cites work: Moreau envelopes of \(s\)-lower regular functions
cites work: A remark on regularization in Hilbert spaces
cites work: Practical Aspects of the Moreau--Yosida Regularization: Theoretical Preliminaries
cites work: Partial Extensions of Attouch's Theorem with Applications to Proto- Derivatives of Subgradient Mappings
cites work: Regularization by erasement
cites work: Q4903679
cites work: Nonsmooth sequential analysis in Asplund spaces
cites work: Variational Analysis and Generalized Differentiation I
cites work: Q5325793
cites work: Approximately convex functions and approximately monotonic operators
cites work: Paraconvex functions and paraconvex sets
cites work: Q5445185
cites work: Subdifferentiation of regularized functions
cites work: Approximation and decomposition properties of some classes of locally d.c. functions
cites work: Proximal mappings
cites work: Calculus Without Derivatives
cites work: Analysis. From concepts to applications
cites work: On the Yosida approximation of operators
cites work: Integration of subdifferentials of nonconvex functions
cites work: An Extension of Attouch's Theorem and Its Application to Second-Order Epi-Differentiation of Convexly Composite Functions
cites work: On the coincidence of some subdifferentials in the class of α(.)-paraconvex functions

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cites work: Q4352477

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cites work: Integration of subdifferentials of lower semicontinuous functions on Banach spaces

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cites work: Strong and Weak Convexity of Sets and Functions

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cites work: Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces

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cites work: Q3149262

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cites work: On various semiconvex relaxations of the squared-distance function

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cites work: Compensated convexity and its applications

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cites work: Compensated Convexity, Multiscale Medial Axis Maps and Sharp Regularity of the Squared-Distance Function

Helping you finding an appropriate regularization process (Wikidata QID)
Wikidata QID: Q129979555

Helping you finding an appropriate regularization process (DOI)
DOI: 10.1007/S10013-018-0293-Z