Implicit functions and solution mappings: a view from variational analysis
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2009
|
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | lizenzfrei Inhaltsverzeichnis |
| Beschreibung: | XII, 375 S. Ill., graph. Darst. 235 mm x 155 mm |
| ISBN: | 9780387878201 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804139291069120512 |
|---|---|
| adam_text | Titel: Implicit functions and solution mappings
Autor: Dončev, Asen L.
Jahr: 2009
Contents
Preface v
Acknowledgements ix
Chapter 1. Functions defined implicitly by equations I
1 A. The classical inverse function theorem 9
IB. The classical implicit function theorem 17
1C. Calmness 21
ID. Lipschitz continuity 26
IE. Lipschitz invertibility from approximations 35
1F. Selections of multi-valued inverses 47
1G. Selections from nonstrict differentiability 51
Chapter 2. Implicit function theorems for variational problems 61
2A. Generalized equations and variational problems 62
2B. Implicit function theorems for generalized equations 74
2C. Ample parameterization and parametric robustness 83
2D. Semidifferentiable functions 88
2E. Variational inequalities with polyhedral convexity 95
2F. Variational inequalities with monotonicity 106
2G. Consequences for optimization 112
Chapter 3. Regularity properties of set-valued solution mappings 131
3A. Set convergence 134
3B. Continuity of set-valued mappings 142
3C. Lipschitz continuity of set-valued mappings 148
3D. Outer Lipschitz continuity 154
Contents
3E. Aubin property, metric regularity and linear openness 159
3F. Implicit mapping theorems with metric regularity 169
3G. Strong metric regularity 178
3H. Calmness and metric subregularity 182
31. Strong metric subregularity 186
Chapter 4. Regularity properties through generalized derivatives 197
4A. Graphical differentiation 198
4B. Derivative criteria for the Aubin property 205
4C. Characterization of strong metric subregularity 217
4D. Applications to parameterized constraint systems 221
4E. Isolated calmness for variational inequalities 224
4F. Single-valued localizations for variational inequalities 228
4G. Special nonsmooth inverse function theorems 237
4H. Results utilizing coderivatives 245
Chapter 5. Regularity in infinite dimensions 251
5A. Openness and positively homogeneous mappings 253
5B. Mappings with closed and convex graphs 259
5C. Sublinear mappings 265
5D. The theorems of Lyusternik and Graves 274
5E. Metric regularity in metric spaces 280
5F. Strong metric regularity and implicit function theorems 292
5G. The Bartle-Graves theorem and extensions 297
Chapter 6. Applications in numerical variational analysis 311
6A. Radius theorems and conditioning 312
6B. Constraints and feasibility 320
6C. Iterative processes for generalized equations 326
6D. An implicit function theorem for Newton s iteration 336
6E. Galerkin s method for quadratic minimization 348
6F. Approximations in optimal control 352
References 363
Notation 371
Index 373
|
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| discipline | Mathematik |
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| indexdate | 2024-07-09T21:41:45Z |
| institution | BVB |
| isbn | 9780387878201 |
| language | English |
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| spelling | Dončev, Asen L. 1948- Verfasser (DE-588)110480376 aut Implicit functions and solution mappings a view from variational analysis Asen L. Dontchev ; R. Tyrrell Rockafeller New York, NY Springer 2009 XII, 375 S. Ill., graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Implizite Funktion (DE-588)4570203-2 gnd rswk-swf Variationsproblem (DE-588)4187419-5 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Implizite Funktion (DE-588)4570203-2 s Variationsproblem (DE-588)4187419-5 s Variationsrechnung (DE-588)4062355-5 s DE-604 Rockafellar, Ralph Tyrrell 1935- Verfasser (DE-588)115723498 aut Erscheint auch als Online-Ausgabe 978-0-387-87821-8 http://www.gbv.de/dms/ilmenau/toc/576933279.PDF lizenzfrei HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017675701&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dončev, Asen L. 1948- Rockafellar, Ralph Tyrrell 1935- Implicit functions and solution mappings a view from variational analysis Implizite Funktion (DE-588)4570203-2 gnd Variationsproblem (DE-588)4187419-5 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4570203-2 (DE-588)4187419-5 (DE-588)4062355-5 (DE-588)4123623-3 |
| title | Implicit functions and solution mappings a view from variational analysis |
| title_auth | Implicit functions and solution mappings a view from variational analysis |
| title_exact_search | Implicit functions and solution mappings a view from variational analysis |
| title_full | Implicit functions and solution mappings a view from variational analysis Asen L. Dontchev ; R. Tyrrell Rockafeller |
| title_fullStr | Implicit functions and solution mappings a view from variational analysis Asen L. Dontchev ; R. Tyrrell Rockafeller |
| title_full_unstemmed | Implicit functions and solution mappings a view from variational analysis Asen L. Dontchev ; R. Tyrrell Rockafeller |
| title_short | Implicit functions and solution mappings |
| title_sort | implicit functions and solution mappings a view from variational analysis |
| title_sub | a view from variational analysis |
| topic | Implizite Funktion (DE-588)4570203-2 gnd Variationsproblem (DE-588)4187419-5 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Implizite Funktion Variationsproblem Variationsrechnung Lehrbuch |
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