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Pełne teksty:
Warianty tytułu
Abstrakty
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
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
Słowa kluczowe
Tematy
Kategoryzacja MSC:
- 49L25: Viscosity solutions
- 49J45: Methods involving semicontinuity and convergence; relaxation
- 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
- 65K10: Optimization and variational techniques
- 54B20: Hyperspaces
- 52A41: Convex functions and convex programs
- 49J27: Problems in abstract spaces
- 46N10: Applications in optimization, convex analysis, mathematical programming, economics
- 49J50: Fr\'echet and Gateaux differentiability
- 52A40: Inequalities and extremum problems
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
autor
- Department of Mathematics, University of Lund, P.O. Box 118, S-221 00 Lund, Sweden
Bibliografia
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Języki publikacji
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Uwagi
1991 Mathematics Subject Classification: 41A65, 46N10, 49J27, 49J45, 49J50, 49L25, 52A40, 52A41, 54B20, 65K10.
Identyfikator YADDA
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ISSN
0012-3862
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DML-PL
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