Approximation methods in optimization of nonlinear systems:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin
De Gruyter
[2020]
|
| Schriftenreihe: | De Gruyter series in nonlinear analysis and applications
volume 32 |
| Schlagwörter: | |
| Links: | https://d-nb.info/1194568386/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032035516&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIII, 338 Seiten Illustrationen, Diagramme |
| ISBN: | 9783110668438 3110668432 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV046623833 | ||
| 003 | DE-604 | ||
| 005 | 20230120 | ||
| 007 | t| | ||
| 008 | 200311s2020 gw a||| |||| 00||| eng d | ||
| 015 | |a 19,N38 |2 dnb | ||
| 015 | |a 20,A03 |2 dnb | ||
| 016 | 7 | |a 1194568386 |2 DE-101 | |
| 020 | |a 9783110668438 |c hardcover |9 978-3-11-066843-8 | ||
| 020 | |a 3110668432 |c hardcover |9 3-11-066843-2 | ||
| 024 | 3 | |a 9783110668438 | |
| 035 | |a (OCoLC)1119748889 | ||
| 035 | |a (DE-599)DNB1194568386 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-20 |a DE-11 | ||
| 082 | 0 | |a 515.353 |2 23/ger | |
| 084 | |a SK 540 |0 (DE-625)143245: |2 rvk | ||
| 084 | |a SK 880 |0 (DE-625)143266: |2 rvk | ||
| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Kogut, Peter I. |e Verfasser |0 (DE-588)120251717X |4 aut | |
| 245 | 1 | 0 | |a Approximation methods in optimization of nonlinear systems |c Peter I. Kogut, Olha P. Kupenko |
| 264 | 1 | |a Berlin |b De Gruyter |c [2020] | |
| 264 | 4 | |c © 2020 | |
| 300 | |a XIII, 338 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter series in nonlinear analysis and applications |v volume 32 | |
| 650 | 0 | 7 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare partielle Differentialgleichung |0 (DE-588)4128900-6 |2 gnd |9 rswk-swf |
| 653 | |a Optimierungstheorie | ||
| 653 | |a Nichtlineare elliptische Differentialgleichung | ||
| 653 | |a Nichtlineare parabolische Differentialgleichung | ||
| 689 | 0 | 0 | |a Nichtlineare partielle Differentialgleichung |0 (DE-588)4128900-6 |D s |
| 689 | 0 | 1 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Kupenko, Olha P. |e Verfasser |0 (DE-588)1202517285 |4 aut | |
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-3-11-066859-9 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 978-3-11-066843-8 |
| 830 | 0 | |a De Gruyter series in nonlinear analysis and applications |v volume 32 |w (DE-604)BV005530011 |9 32 | |
| 856 | 4 | 2 | |m B:DE-101 |q application/pdf |u https://d-nb.info/1194568386/04 |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032035516&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-032035516 | |
Datensatz im Suchindex
| _version_ | 1819361184505135104 |
|---|---|
| adam_text | CONTENTS
PREFACE
*
VII
INTRODUCTION
*
1
1
OPTIMAL
DISTRIBUTED
CONTROL
PROBLEM
FOR
AN
ILL-POSED
STRONGLY
NONLINEAR
ELLIPTIC
EQUATION
WITH
P-LAPLACE
OPERATOR
AND
I?-TYPE
OF
NONLINEARITY
*
11
1.1
AUXILIARIES
AND
PREVIOUS
ANALYSIS
OF
THE
BOUNDARY
VALUE
PROBLEM
*
12
1.2
ON
POHOZAEV
INEQUALITY
AND
A
PRIORI
ESTIMATES
FORA
SPECIAL
CLASS
OF
WEAK
SOLUTIONS
*
16
1.3
ON
REFORMULATION
OF
THE
ORIGINAL
OPTIMAL
CONTROL
PROBLEM
*
25
1.4
AUXILIARY
FICTITIOUS
OPTIMAL
CONTROL
PROBLEM
AND
ITS
PROPERTIES
*
27
1.5
ON
A
PRIORI
ESTIMATE
FOR
THE
SOLUTIONS
OF
VARIATIONAL
PROBLEM
(1.59)
*
29
1.6
ON
ASYMPTOTIC
BEHAVIOUR
OF
THE
SEQUENCE
OF
OPTIMAL
PAIRS
TO
THE
PROBLEM
(1.47)-(1.50)
AS
-
0
-----
34
2
ON
APPROXIMATION
OF
ONE
CLASS
OF
OPTIMAL
CONTROL
PROBLEMS
FOR
STRONGLY
NONLINEAR
ELLIPTIC
EQUATIONS
WITH
P-LAPLACE
OPERATOR
*
39
2.1
ON
CONSISTENCY
OF
OPTIMAL
CONTROL
PROBLEM
*
40
2.2
APPROXIMATING
OPTIMAL
CONTROL
PROBLEMS
AND
THEIR
PREVIOUS
ANALYSIS
*
44
2.3
ASYMPTOTIC
ANALYSIS
OF
APPROXIMATING
OCP
*
54
2.4
OPTIMALITY
CONDITIONS
FOR
APPROXIMATING
OCP
*
67
3
NEUMANN
BOUNDARY
OPTIMAL
CONTROL
PROBLEM
FOR
STRONGLY
NONLINEAR
ELLIPTIC
EQUATION
WITH
P-LAPLACE
OPERATOR
*
73
3.1
SETTING
OF
THE
PROBLEM
*
74
3.2
A
PRIORI
ESTIMATES
BOTH
FOR
ENERGY
SOLUTIONS
AND
FEASIBLE
SOLUTIONS
*
80
3.3
EXISTENCE
OF
OPTIMAL
BOUNDARY
CONTROLS
*
96
3.4
ON
APPROXIMATION
OF
OPTIMAL
BOUNDARY
CONTROL
PROBLEM
*
98
3.5
ON
EXISTENCE
OF
BOUNDED
FEASIBLE
SOLUTIONS
*
108
4
ASYMPTOTIC
ANALYSIS
OF
OPTIMAL
NEUMANN
BOUNDARY
CONTROL
PROBLEM
IN
DOMAIN
WITH
BOUNDARY
OSCILLATION
FOR
ELLIPTIC
EQUATION
WITH
EXPONENTIAL
NON-LINEARITY
*
116
4.1
PREVIOUS
ANALYSIS
OF
OPTIMAL
CONTROL
PROBLEM
*
118
4.2
ON
CONSISTENCY
OF
OPTIMAL
CONTROL
PROBLEM
*
129
4.3
ON
UNIQUENESS
OF
OPTIMAL
SOLUTION
AND
OPTIMALITY
CONDITIONS
*
133
4.4
DESCRIPTION
OF
THE
DOMAIN
PERTURBATIONS
*
141
4.5
ASYMPTOTIC
ANALYSIS
OF
OCP
(4.1)-(4.5)
-----
147
XII
*
CONTENTS
5
ON
OPTIMAL
AND
QUASI-OPTIMAL
CONTROLS
IN
COEFFICIENTS
FOR
MULTI-DIMENSIONAL
THERMISTOR
PROBLEM
WITH
MIXED
DIRICHLET-NEUMANN
BOUNDARY
CONDITIONS
*
164
5.1
INTRODUCTION
AND
MAIN
MOTIVATION
*
164
5.1.1
RELAXATION
OF
THE
ORIGINAL
OCR
*
170
5.1.2
MOTIVATION
-----
172
5.1.3
MAIN
RESULTS
-----
173
5.2
PRELIMINARIES
AND
SOME
AUXILIARY
RESULTS
*
174
5.2.1
ON
ORLICZ
SPACES
*
174
5.2.2
SOME
SPECIAL
PROPERTIES
OF
SOBOLEV-ORLICZ
SPACES
*
179
5.2.3
ON
THE
WEAK
CONVERGENCE
OF
FLUXES
TO
FLUX
*
183
5.3
ON
APPROXIMATED
OPTIMAL
CONTROL
PROBLEM
IN
COEFFICIENTS
AND
ITS
PROPERTIES
*
187
5.4
ASYMPTOTIC
ANALYSIS
OF
OCR
(5.19)-(5.23)
-----
198
6
APPROXIMATION
OF
AN
OPTIMAL
CONTROL
PROBLEM
IN
COEFFICIENT
FOR
VARIATIONAL
INEQUALITY
WITH
ANISOTROPIC
P-LAPLACIAN
*
211
6.1
SETTING
OF
THE
OPTIMAL
CONTROL
PROBLEM
*
212
6.2
EXISTENCE
OF
OPTIMAL
SOLUTIONS
*
216
6.3
REGULARIZATION
OF
OCR
*
218
6.4
ASYMPTOTIC
ANALYSIS
OF
APPROXIMATING
OCR
*
222
7
ON
UNBOUNDED
OPTIMAL
CONTROLS
IN
COEFFICIENTS
FOR
ILL-POSED
ELLIPTIC
DIRICHLET
BOUNDARY
VALUE
PROBLEMS
*
226
7.1
NOTATION
AND
PRELIMINARIES
*
227
7.2
WEAK
CONVERGENCE
IN
VARIABLE
2
-SPACES
ASSOCIATED
WITH
S$YM-MATRICES
*
233
7.3
SETTING
OF
THE
OPTIMAL
CONTROL
PROBLEM
*
236
7.4
ON
VARIATIONAL
SOLUTIONS
TO
OCR
(7.1)-(7.3)
AND
THEIR
APPROXIMATION
*
244
7.5
ON
ATTAINABILITY
OF
NON-VARIATIONAL
OPTIMAL
SOLUTIONS
*
261
7.6
ON
SOME
PROPERTIES
OF
UNBOUNDED
BILINEAR
FORMS
ASSOCIATED
WITH
SKEW-SYMMETRIC
2
(O)-MATRICES
*
278
7.6.1
PRELIMINARIES
*
279
7.6.2
MOTIVATING
EXAMPLE
*
282
7.6.3
ON
FORMULA
OF
INTEGRATION
BY
PARTS
FOR
MEASURABLE
FUNCTIONS
*
287
7.6.4
ON
SUBSTANTIATION
OF
FORMULA
(7.198)
FOR
A
NON-LIPSCHITZ
CASE
*
289
7.6.5
PROOF
OF
THE
UNIQUENESS
RESULT
*
290
8
ON
OPTIMAL
P-CONTROL
IN
COEFFICIENTS
FOR
QUASI-LINEAR
DIRICHLET
BOUNDARY
VALUE
PROBLEM
WITH
BMO-ANISOTROPIC
P-LAPLACIAN
*
294
8.1
NOTATION
AND
PRELIMINARIES
*
296
CONTENTS
*
XIII
BIBLIOGRAPHY
*
331
8.2
8.3
8.4
8.5
SETTING
OF
THE
OPTIMAL
CONTROL
PROBLEM
*
301
ON
CONSISTENCY
OF
OPTIMAL
CONTROL
PROBLEM
(8.28)-(8.31)
-----
305
EXISTENCE
OF
OPTIMAL
PAIRS
*
314
ON
HIGHER
INTEGRABILITY
OF
THE
GRADIENT
OF
AN
APPROXIMATION
SOLUTION
-----
316
8.6
ON
DENSITY
OF
SMOOTH
COMPACTLY
SUPPORTED
FUNCTIONS
IN
W*
P
B
(Q)
*
325
|
| any_adam_object | 1 |
| author | Kogut, Peter I. Kupenko, Olha P. |
| author_GND | (DE-588)120251717X (DE-588)1202517285 |
| author_facet | Kogut, Peter I. Kupenko, Olha P. |
| author_role | aut aut |
| author_sort | Kogut, Peter I. |
| author_variant | p i k pi pik o p k op opk |
| building | Verbundindex |
| bvnumber | BV046623833 |
| classification_rvk | SK 540 SK 880 |
| ctrlnum | (OCoLC)1119748889 (DE-599)DNB1194568386 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02494nam a2200577 cb4500</leader><controlfield tag="001">BV046623833</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230120 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">200311s2020 gw a||| |||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">19,N38</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">20,A03</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">1194568386</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110668438</subfield><subfield code="c">hardcover</subfield><subfield code="9">978-3-11-066843-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3110668432</subfield><subfield code="c">hardcover</subfield><subfield code="9">3-11-066843-2</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9783110668438</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1119748889</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB1194568386</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE-BE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.353</subfield><subfield code="2">23/ger</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 540</subfield><subfield code="0">(DE-625)143245:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 880</subfield><subfield code="0">(DE-625)143266:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kogut, Peter I.</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)120251717X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Approximation methods in optimization of nonlinear systems</subfield><subfield code="c">Peter I. Kogut, Olha P. Kupenko</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin</subfield><subfield code="b">De Gruyter</subfield><subfield code="c">[2020]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2020</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 338 Seiten</subfield><subfield code="b">Illustrationen, Diagramme</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">De Gruyter series in nonlinear analysis and applications</subfield><subfield code="v">volume 32</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Optimale Kontrolle</subfield><subfield code="0">(DE-588)4121428-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4128900-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Optimierungstheorie</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Nichtlineare elliptische Differentialgleichung</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Nichtlineare parabolische Differentialgleichung</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtlineare partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4128900-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Optimale Kontrolle</subfield><subfield code="0">(DE-588)4121428-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kupenko, Olha P.</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1202517285</subfield><subfield code="4">aut</subfield></datafield><datafield tag="710" ind1="2" ind2=" "><subfield code="a">Walter de Gruyter GmbH & Co. KG</subfield><subfield code="0">(DE-588)10095502-2</subfield><subfield code="4">pbl</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe, EPUB</subfield><subfield code="z">978-3-11-066859-9</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe, PDF</subfield><subfield code="z">978-3-11-066843-8</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">De Gruyter series in nonlinear analysis and applications</subfield><subfield code="v">volume 32</subfield><subfield code="w">(DE-604)BV005530011</subfield><subfield code="9">32</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">B:DE-101</subfield><subfield code="q">application/pdf</subfield><subfield code="u">https://d-nb.info/1194568386/04</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032035516&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-032035516</subfield></datafield></record></collection> |
| id | DE-604.BV046623833 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T18:56:35Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110668438 3110668432 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032035516 |
| oclc_num | 1119748889 |
| open_access_boolean | |
| owner | DE-20 DE-11 |
| owner_facet | DE-20 DE-11 |
| physical | XIII, 338 Seiten Illustrationen, Diagramme |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter series in nonlinear analysis and applications |
| series2 | De Gruyter series in nonlinear analysis and applications |
| spellingShingle | Kogut, Peter I. Kupenko, Olha P. Approximation methods in optimization of nonlinear systems De Gruyter series in nonlinear analysis and applications Optimale Kontrolle (DE-588)4121428-6 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4121428-6 (DE-588)4128900-6 |
| title | Approximation methods in optimization of nonlinear systems |
| title_auth | Approximation methods in optimization of nonlinear systems |
| title_exact_search | Approximation methods in optimization of nonlinear systems |
| title_full | Approximation methods in optimization of nonlinear systems Peter I. Kogut, Olha P. Kupenko |
| title_fullStr | Approximation methods in optimization of nonlinear systems Peter I. Kogut, Olha P. Kupenko |
| title_full_unstemmed | Approximation methods in optimization of nonlinear systems Peter I. Kogut, Olha P. Kupenko |
| title_short | Approximation methods in optimization of nonlinear systems |
| title_sort | approximation methods in optimization of nonlinear systems |
| topic | Optimale Kontrolle (DE-588)4121428-6 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Optimale Kontrolle Nichtlineare partielle Differentialgleichung |
| url | https://d-nb.info/1194568386/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032035516&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005530011 |
| work_keys_str_mv | AT kogutpeteri approximationmethodsinoptimizationofnonlinearsystems AT kupenkoolhap approximationmethodsinoptimizationofnonlinearsystems AT walterdegruytergmbhcokg approximationmethodsinoptimizationofnonlinearsystems |