Stable methods for ill-posed variational problems: prox-regularization of elliptic variational inequalities and semi-infinite problems
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Berlin
Akad.-Verl.
1994
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Mathematical topics
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 437 S. graph. Darst. |
| ISBN: | 3055016351 |
Internformat
MARC
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| 100 | 1 | |a Kaplan, Aleksandr A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stable methods for ill-posed variational problems |b prox-regularization of elliptic variational inequalities and semi-infinite problems |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin |b Akad.-Verl. |c 1994 | |
| 300 | |a 437 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804136132414275584 |
|---|---|
| adam_text | CONTENTS
CHAPTER I ILL POSED PROBLEMS AND THEIR STABILIZATION
1 Concepts of Well Posedness Examples of Ill Posed Problems .... 11
2 Well and Ill Posed Variational Problems 17
3 Approaches of Stabilizing Ill Posed Problems 28
CHAPTER II STABLE DISCRETIZATION AND SOLUTION METHODS
FOR ILL POSED VARIATIONAL PROBLEMS
4 Stabilizing Properties of Some Numerical Methods 45
5 Stabilization of Problems and of Numerical Methods 56
6 Iterative Regularization Methods Based on Tikhonov s Principle . . 60
7 Mosco s Approximation Scheme 70
CHAPTER III THE METHOD OF ITERATIVE PROX REGULARIZATION
FOR FINITE DIMENSIONAL PROBLEMS
8 Properties of the Prox Mapping 77
9 Algorithms for Finite Dimensional Convex Optimization Problems . . 81
10 Effect of Prox Regularization in Methods of Numerical Analysis . . 102
CHAPTER IV ITERATIVE PROX REGULARIZATION FOR INFINITE
DIMENSIONAL PROBLEMS
11 Preliminary Results 106
12 One Step Regularisation Methods 110
13 Multi Step Regularization Methods 123
CHAPTER V RATE OF CONVERGENCE OF ITERATIVE
PROX REGULARIZATION METHODS
14 Rate of Convergence of MSR Methods 147
15 Rate of Convergence of OSR Methods 171
16 Rate of Convergence of Regularized Penalty Methods 174
10 CONTENTS
CHAPTER VI ITERATIVE PROX REGULARIZATION FOR CONVEX
SEMI INFINITE PROGRAMMING PROBLEMS
17 Introduction to the Numerical Treatment of Semi Infinite
Programming Problems 178
18 Stable Methods for Ill Posed Convex Semi Infinite Problems 188
19 Convergence Results 203
CHAPTER VII STABLE SOLUTION OF ELLIPTIC VARIATIONAL
INEQUALITIES WITH WEAKLY COERCIVE OPERATORS
20 Approximation of Variational Inequalities 225
21 Contact Problems without Friction 232
22 Three Variants of MSR Methods 244
23 The Special Case of Approximation: K c K 255
i
24 Exactness of the Approximation of Feasible Sets 264
25 Solution of Contact Problems with Friction 270
26 Regularization of Well Posed Problems 278
CHAPTER VIII SOME NUMERICAL ASPECTS
27 Choice of Control Parameters in OSR and MSR methods 283
28 On the Solution of Auxiliary Problems 295
29 Numerical Experiments 298
APPENDIX
Al Some Preliminary Results of Functional Analysis 308
A2 Approximation Techniques and Estimates of Solutions of
Approximate Problems 336
A3 Selected Methods of Convex Optimization 355
COMMENTS 397
REFERENCES 407
SYMBOL INDEX 429
SUBJECT INDEX 433
|
| adam_txt |
CONTENTS
CHAPTER I ILL POSED PROBLEMS AND THEIR STABILIZATION
1 Concepts of Well Posedness Examples of Ill Posed Problems . 11
2 Well and Ill Posed Variational Problems 17
3 Approaches of Stabilizing Ill Posed Problems 28
CHAPTER II STABLE DISCRETIZATION AND SOLUTION METHODS
FOR ILL POSED VARIATIONAL PROBLEMS
4 Stabilizing Properties of Some Numerical Methods 45
5 Stabilization of Problems and of Numerical Methods 56
6 Iterative Regularization Methods Based on Tikhonov's Principle . . 60
7 Mosco's Approximation Scheme 70
CHAPTER III THE METHOD OF ITERATIVE PROX REGULARIZATION
FOR FINITE DIMENSIONAL PROBLEMS
8 Properties of the Prox Mapping 77
9 Algorithms for Finite Dimensional Convex Optimization Problems . . 81
10 Effect of Prox Regularization in Methods of Numerical Analysis . . 102
CHAPTER IV ITERATIVE PROX REGULARIZATION FOR INFINITE
DIMENSIONAL PROBLEMS
11 Preliminary Results 106
12 One Step Regularisation Methods 110
13 Multi Step Regularization Methods 123
CHAPTER V RATE OF CONVERGENCE OF ITERATIVE
PROX REGULARIZATION METHODS
14 Rate of Convergence of MSR Methods 147
15 Rate of Convergence of OSR Methods 171
16 Rate of Convergence of Regularized Penalty Methods 174
10 CONTENTS
CHAPTER VI ITERATIVE PROX REGULARIZATION FOR CONVEX
SEMI INFINITE PROGRAMMING PROBLEMS
17 Introduction to the Numerical Treatment of Semi Infinite
Programming Problems 178
18 Stable Methods for Ill Posed Convex Semi Infinite Problems 188
19 Convergence Results 203
CHAPTER VII STABLE SOLUTION OF ELLIPTIC VARIATIONAL
INEQUALITIES WITH WEAKLY COERCIVE OPERATORS
20 Approximation of Variational Inequalities 225
21 Contact Problems without Friction 232
22 Three Variants of MSR Methods 244
23 The Special Case of Approximation: K c K 255
i
24 Exactness of the Approximation of Feasible Sets 264
25 Solution of Contact Problems with Friction 270
26 Regularization of Well Posed Problems 278
CHAPTER VIII SOME NUMERICAL ASPECTS
27 Choice of Control Parameters in OSR and MSR methods 283
28 On the Solution of Auxiliary Problems 295
29 Numerical Experiments 298
APPENDIX
Al Some Preliminary Results of Functional Analysis 308
A2 Approximation Techniques and Estimates of Solutions of
Approximate Problems 336
A3 Selected Methods of Convex Optimization 355
COMMENTS 397
REFERENCES 407
SYMBOL INDEX 429
SUBJECT INDEX 433 |
| any_adam_object | 1 |
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| author | Kaplan, Aleksandr A. Tichatschke, Rainer 1946- |
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| author_facet | Kaplan, Aleksandr A. Tichatschke, Rainer 1946- |
| author_role | aut aut |
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| bvnumber | BV022157754 |
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| dewey-full | 515/.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.64 |
| dewey-search | 515/.64 |
| dewey-sort | 3515 264 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV022157754 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:18:40Z |
| indexdate | 2024-07-09T20:51:32Z |
| institution | BVB |
| isbn | 3055016351 |
| language | Undetermined |
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| physical | 437 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| publisher | Akad.-Verl. |
| record_format | marc |
| series | Mathematical topics |
| series2 | Mathematical topics |
| spelling | Kaplan, Aleksandr A. Verfasser aut Stable methods for ill-posed variational problems prox-regularization of elliptic variational inequalities and semi-infinite problems 1. ed. Berlin Akad.-Verl. 1994 437 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical topics 3 Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd rswk-swf Variationsungleichung (DE-588)4187420-1 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Elliptisches Variationsproblem (DE-588)4274496-9 gnd rswk-swf Regularisierung (DE-588)4124043-1 gnd rswk-swf Stabilität (DE-588)4056693-6 s DE-604 Variationsungleichung (DE-588)4187420-1 s Elliptisches Variationsproblem (DE-588)4274496-9 s Inkorrekt gestelltes Problem (DE-588)4186951-5 s Regularisierung (DE-588)4124043-1 s 1\p DE-604 Tichatschke, Rainer 1946- Verfasser (DE-588)121208494 aut Mathematical topics 3 (DE-604)BV008671507 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015372420&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kaplan, Aleksandr A. Tichatschke, Rainer 1946- Stable methods for ill-posed variational problems prox-regularization of elliptic variational inequalities and semi-infinite problems Mathematical topics Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd Variationsungleichung (DE-588)4187420-1 gnd Stabilität (DE-588)4056693-6 gnd Elliptisches Variationsproblem (DE-588)4274496-9 gnd Regularisierung (DE-588)4124043-1 gnd |
| subject_GND | (DE-588)4186951-5 (DE-588)4187420-1 (DE-588)4056693-6 (DE-588)4274496-9 (DE-588)4124043-1 |
| title | Stable methods for ill-posed variational problems prox-regularization of elliptic variational inequalities and semi-infinite problems |
| title_auth | Stable methods for ill-posed variational problems prox-regularization of elliptic variational inequalities and semi-infinite problems |
| title_exact_search | Stable methods for ill-posed variational problems prox-regularization of elliptic variational inequalities and semi-infinite problems |
| title_exact_search_txtP | Stable methods for ill-posed variational problems prox-regularization of elliptic variational inequalities and semi-infinite problems |
| title_full | Stable methods for ill-posed variational problems prox-regularization of elliptic variational inequalities and semi-infinite problems |
| title_fullStr | Stable methods for ill-posed variational problems prox-regularization of elliptic variational inequalities and semi-infinite problems |
| title_full_unstemmed | Stable methods for ill-posed variational problems prox-regularization of elliptic variational inequalities and semi-infinite problems |
| title_short | Stable methods for ill-posed variational problems |
| title_sort | stable methods for ill posed variational problems prox regularization of elliptic variational inequalities and semi infinite problems |
| title_sub | prox-regularization of elliptic variational inequalities and semi-infinite problems |
| topic | Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd Variationsungleichung (DE-588)4187420-1 gnd Stabilität (DE-588)4056693-6 gnd Elliptisches Variationsproblem (DE-588)4274496-9 gnd Regularisierung (DE-588)4124043-1 gnd |
| topic_facet | Inkorrekt gestelltes Problem Variationsungleichung Stabilität Elliptisches Variationsproblem Regularisierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015372420&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008671507 |
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