Nonconvex optimal control and variational problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2013
|
| Series: | Springer optimization and its applications
82 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 378 S. |
| ISBN: | 9781461473770 |
Staff View
MARC
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| 100 | 1 | |a Zaslavskij, Aleksandr J. |d 1957- |e Verfasser |0 (DE-588)171024672 |4 aut | |
| 245 | 1 | 0 | |a Nonconvex optimal control and variational problems |c Alexander J. Zaslavski |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2013 | |
| 300 | |a XI, 378 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer optimization and its applications |v 82 | |
| 650 | 0 | 7 | |a Optimierung |0 (DE-588)4043664-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Variationsproblem |0 (DE-588)4187419-5 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Optimierung |0 (DE-588)4043664-0 |D s |
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |t Nonconvex Optimal Control and Variational Problems |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026243022&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Record in the Search Index
| _version_ | 1815536830738595840 |
|---|---|
| adam_text |
Contents
Introduction
. 1
1.1 Generic
Existence of Solutions of Optimal Control Problems
. 1
1.2
Lavrentiev Phenomenon
. 5
1.3
Turnpike Properties
. 10
1.4
Examples
. 12
Well-posedness of Optimal Control Problems
. 17
2.1
Optimal
Control Problems with
Cesari
Growth Condition
. 18
2.2
A Generic Variational Principle
. 24
2.3
Concretization of the Hypothesis (HI)
. 26
2.4
Preliminary Results for Hypotheses (A2) and
(112) . 31
2.5
A Preliminary Lemma for Hypothesis
(A3) . 37
2.6
An Auxiliary Result
. 41
2.7
An Auxiliary Lemma for Hypothesis
(A4). 41
2.8
Proof of Theorem
2.2
and Its Extensions
. 44
2.9
Vaxiational Problems
. 45
2.10
Optimal Control Problems with
Cinquini
Growth Condition
. 49
2.11
Variational Principles
. 54
2.12
Preliminary Results for Theorem
2.20. 56
2.13
Proof of Theorem
2.20. 60
WeU-posedness and Porosity
. 63
3.1
σ
-porous
Sets in a Metric Space
. 64
3.2
Well-posedness of Optimization Problems
. 66
3.3
A Variational Principle
. 68
3.4
Well-posedness Results
. 73
3.5
A Preliminary Result for Theorems
3.9
and
3.10. 80
3.6
An Auxiliary Result for Theorem
3.10. 84
3.7
Proofs of Theorems
3.9
and
3.10. 85
WelJ-posedness of Nonconvex Variational Problems
. 87
4.1
Two Classes of Variational Problems
. 87
4.2
Variational Principles
.-. 88
ix
Contents
4.3
Proof of Proposition
4.1. 89
4.4
Genene
Well-posed ness Results
. 92
4.5
Proofs of Theorems
4.6
and
4.7 . 97
4.6
Porous Sets and Well-posedness
. 104
4.7
A Variational Principle
. 106
4.8
Well-posedness and Porosity in the Calculus of Variations
.
Ill
4.9
Preliminary Results for Hypotheses
(Al),
(A3),
and (H)
. 115
4.10
An Auxiliary Result for Hypothesis
(A4). 117
4.11
Proof of Theorem
4.20. 122
5
Generic Well-posedness Result
. 125
5.1
Preliminaries
. 125
5.2
Concretization of the Hypothesis (HI)
. 126
5.3
Generic Well-posedness
. 131
5.4
A Class of Differential Equations
. 136
5.5
An Auxiliary Result for (A5)
. 142
5.6
Auxiliary Results for
(A4). 145
5.7
Proof of Proposition
5.3. 151
5.8
Auxiliary Results for (H2) and (A1)-(A4)
. 154
5.9
Proof of Theorem
5.4 . 156
5.10
An Extension of Theorem
5.4 . 157
6
Nonoccurrence of the Lavrentiev Phenomenon
for Variational Problems
. 159
6.1
Spaces of Integrands
. 159
6.2
Auxiliary Results
. 164
63
Proof of Theorem
6.2 . 165
6.4
An Auxiliary Result for Theorem
6.7. 175
6.5
Proof of Proposition
6.4. 181
6.6
Proofs of Theorems
6.5-6.7 . 182
6.7
Proofs of Theorems
6.8
and
6.9 . 185
6.8
Generic Existence of Lipschitzian Solutions
. 189
7
Nonoccurrence of the Lavrentiev Phenomenon in Optimal Control
. 197
7.1
Preliminaries, Assumptions, and Main Results
. 197
7.2
Auxiliary Results
. 205
7.3
Proofs of Theorems
7.4
and
7.5 . 209
7.4
Proofs of Theorems
7.6
and
7.7 . 214
7.5
A Density Result
. 219
7.6
Proofs of Theorems
7.8-7.10. 224
7.7
Examples
. 226
7.8
Sarychev Integrands
. 228
8
Generic Nonoccurrence of the Lavrentiev Phenomenon
. 233
8.1
Preliminaries, Assumptions, and Main Results
. 233
8.2
Auxiliary Results
. 240
8.3
Proofs of Theorems
8.2-8.3 . 252
Contents
χι
9
Infini te
-D
im
ens
і
on
al Linear
Control Problems
. 255
9.1
Preliminaries, Assumptions, and Main Results
. 255
9.2
Auxiliary Results
. 261
9.3
Proof of Theorem
9.1 . 263
9.4
An Auxiliary Result for Theorem
9.5. 273
9.5
Proof of Lemma
9.2. 280
9.6
Proofs of Theorems of
9.3-9.5 . 281
10
Uniform Boundedness of Approximate Solutions
of VariationaJ Problems
. 285
10.1
Preliminaries and Main Results
. 285
10.2
Preliminary Results
. 289
10.3
Discrete -Time Control Systems
. 294
10.4
Proofs of Theorems
10.1, 10.3,
and
10.4. 297
11
The Turnpike Property for Approximate Solutions
. 305
11.1
Preliminaries and Mam Results
. 305
11.2
Auxiliary Results for the Main Theorems
. 308
11.3
Proofs of Theorems
11.1-11.3. 322
12
A Turnpike Result for Optimal Control Systems
. 327
12.1
Discrete-Time Optimal Control Systems
. 327
12.2
The
Genene
Turnpike Result
. 329
12.3
Preliminaries
. 331
12.4
Auxiliary Results
. 339
12.5
Proof of Theorem
12.1. 366
References
. 371
Index
. 377 |
| any_adam_object | 1 |
| author | Zaslavskij, Aleksandr J. 1957- |
| author_GND | (DE-588)171024672 |
| author_facet | Zaslavskij, Aleksandr J. 1957- |
| author_role | aut |
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| bvnumber | BV041269386 |
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| ctrlnum | (OCoLC)859397933 (DE-599)BSZ391157493 |
| discipline | Mathematik |
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| id | DE-604.BV041269386 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-12T17:00:45Z |
| institution | BVB |
| isbn | 9781461473770 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026243022 |
| oclc_num | 859397933 |
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| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XI, 378 S. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer optimization and its applications |
| spelling | Zaslavskij, Aleksandr J. 1957- Verfasser (DE-588)171024672 aut Nonconvex optimal control and variational problems Alexander J. Zaslavski New York [u.a.] Springer 2013 XI, 378 S. txt rdacontent n rdamedia nc rdacarrier Springer optimization and its applications 82 Optimierung (DE-588)4043664-0 gnd rswk-swf Variationsproblem (DE-588)4187419-5 gnd rswk-swf Variationsproblem (DE-588)4187419-5 s Optimierung (DE-588)4043664-0 s DE-604 Erscheint auch als Online-Ausgabe Nonconvex Optimal Control and Variational Problems Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026243022&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zaslavskij, Aleksandr J. 1957- Nonconvex optimal control and variational problems Optimierung (DE-588)4043664-0 gnd Variationsproblem (DE-588)4187419-5 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4187419-5 |
| title | Nonconvex optimal control and variational problems |
| title_auth | Nonconvex optimal control and variational problems |
| title_exact_search | Nonconvex optimal control and variational problems |
| title_full | Nonconvex optimal control and variational problems Alexander J. Zaslavski |
| title_fullStr | Nonconvex optimal control and variational problems Alexander J. Zaslavski |
| title_full_unstemmed | Nonconvex optimal control and variational problems Alexander J. Zaslavski |
| title_short | Nonconvex optimal control and variational problems |
| title_sort | nonconvex optimal control and variational problems |
| topic | Optimierung (DE-588)4043664-0 gnd Variationsproblem (DE-588)4187419-5 gnd |
| topic_facet | Optimierung Variationsproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026243022&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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