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The operation of infimal convolution

Seria
Rozprawy Matematyczne tom/nr w serii: 352 wydano: 1996
Zawartość
Warianty tytułu
Abstrakty
EN
Abstract
This 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.
EN
CONTENTS
1. Introduction and preliminaries....................................................5
 1.1. Introduction............................................................................5
 1.2. Organization..........................................................................6
 1.3. Prerequisites.........................................................................6
 1.4. Introductory examples...........................................................9
2. 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......................................................................22
3. 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.........................................................32
4. 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.................................................39
5. Regularization.........................................................................41
 5.1. Introduction and first results................................................41
 5.2. Approximation in Hilbert spaces...........................................47
 5.3. Generalized Moreau-Yosida approximation.........................52
References..................................................................................55
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 352
Liczba stron
58
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCLI
Daty
wydano
1996
otrzymano
1994-08-16
poprawiono
1995-03-17
Twórcy
  • Department of Mathematics, University of Lund, P.O. Box 118, S-221 00 Lund, Sweden, thomas@maths.lth.se
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Języki publikacji
EN
Uwagi
1991 Mathematics Subject Classification: 41A65, 46N10, 49J27, 49J45, 49J50, 49L25, 52A40, 52A41, 54B20, 65K10.
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0012-3862
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DML-PL
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