The operation of infimal convolution

Strömberg Thomas. The operation of infimal convolution. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1996. <http://eudml.org/doc/271746>.

@book{StrömbergThomas1996,
abstract = {AbstractThis paper is a survey article on the theory and applications of infimal convolution. We consider the convex as well as the nonconvex case. In particular, we provide a detailed investigation of the regularizing effects of infimal convolution, and study continuity properties of the operation with respect to notions of variational convergence. Several examples are included and well-known results are complemented, unified or extended in various ways.CONTENTS1. Introduction and preliminaries....................................................5 1.1. Introduction............................................................................5 1.2. Organization..........................................................................6 1.3. Prerequisites.........................................................................6 1.4. Introductory examples...........................................................92. Elementary properties.............................................................14 2.1. Basic facts...........................................................................14 2.2. Infimal convolution of subadditive functions.........................17 2.3. Semicontinuity, continuity, and exactness............................19 2.4. Two examples......................................................................223. The convex case.....................................................................23 3.1. Basic results........................................................................23 3.2. Differential calculus, and first order differentiability..............28 3.3. Formulas on f ▫ g.................................................................31 3.4. Loss of differentiability.........................................................324. Continuity of the operation of infimal convolution....................33 4.1. Introduction.........................................................................34 4.2. Epi-convergence.................................................................35 4.3. The Mosco topology and the slice topology.........................36 4.4. The affine topology..............................................................38 4.5. The Attouch-Wets topology.................................................395. Regularization.........................................................................41 5.1. Introduction and first results................................................41 5.2. Approximation in Hilbert spaces...........................................47 5.3. Generalized Moreau-Yosida approximation.........................52References..................................................................................551991 Mathematics Subject Classification: 41A65, 46N10, 49J27, 49J45, 49J50, 49L25, 52A40, 52A41, 54B20, 65K10.},
author = {Strömberg Thomas},
keywords = {infimal convolution; epigraphical addition; regularization; approximation; variational convergence; survey; regularizing effect; epi-convergence; slice topology; affine topology; Attouch-Wets topology; Moreau-Yosida approximation},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {The operation of infimal convolution},
url = {http://eudml.org/doc/271746},
year = {1996},
}

TY - BOOK
AU - Strömberg Thomas
TI - The operation of infimal convolution
PY - 1996
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - AbstractThis paper is a survey article on the theory and applications of infimal convolution. We consider the convex as well as the nonconvex case. In particular, we provide a detailed investigation of the regularizing effects of infimal convolution, and study continuity properties of the operation with respect to notions of variational convergence. Several examples are included and well-known results are complemented, unified or extended in various ways.CONTENTS1. Introduction and preliminaries....................................................5 1.1. Introduction............................................................................5 1.2. Organization..........................................................................6 1.3. Prerequisites.........................................................................6 1.4. Introductory examples...........................................................92. Elementary properties.............................................................14 2.1. Basic facts...........................................................................14 2.2. Infimal convolution of subadditive functions.........................17 2.3. Semicontinuity, continuity, and exactness............................19 2.4. Two examples......................................................................223. The convex case.....................................................................23 3.1. Basic results........................................................................23 3.2. Differential calculus, and first order differentiability..............28 3.3. Formulas on f ▫ g.................................................................31 3.4. Loss of differentiability.........................................................324. Continuity of the operation of infimal convolution....................33 4.1. Introduction.........................................................................34 4.2. Epi-convergence.................................................................35 4.3. The Mosco topology and the slice topology.........................36 4.4. The affine topology..............................................................38 4.5. The Attouch-Wets topology.................................................395. Regularization.........................................................................41 5.1. Introduction and first results................................................41 5.2. Approximation in Hilbert spaces...........................................47 5.3. Generalized Moreau-Yosida approximation.........................52References..................................................................................551991 Mathematics Subject Classification: 41A65, 46N10, 49J27, 49J45, 49J50, 49L25, 52A40, 52A41, 54B20, 65K10.
LA - eng
KW - infimal convolution; epigraphical addition; regularization; approximation; variational convergence; survey; regularizing effect; epi-convergence; slice topology; affine topology; Attouch-Wets topology; Moreau-Yosida approximation
UR - http://eudml.org/doc/271746
ER -