Optimal and suboptimal control of partial differential equations: augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Graz
Fachbibl. für Mathematik, Univ.
2001
|
| Series: | Grazer mathematische Berichte
343 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 131 S. |
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| 245 | 1 | 0 | |a Optimal and suboptimal control of partial differential equations |b augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition |c Stefan Volkwein |
| 264 | 1 | |a Graz |b Fachbibl. für Mathematik, Univ. |c 2001 | |
| 300 | |a VI, 131 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
1
Preface
1
1.1 Motivation.................................. 1
1.2
Notations
.................................. 2
2
The augmented Lagrange-SQP method
4
2.1
Introduction
................................. 4
2.2
The augmented Lagrange-SQP algorithm
................. 7
2.3
The Newton
Lagrange
multiplier update
................. 12
2.4
The Lipschitz-continuous
Lagrange
multiplier update
.......... 15
2.4.1
Local convergence results
...................... 15
2.4.2
Problems with representation for the null space of the linearized
constraint
.............................. 18
2.5 Affine
invariant convergence analysis
................... 20
2.5.1 Affine
invariance..........................
20
2.5.2
Affine
invariant convergence theory
................ 22
2.5.3
Inexact augmented Lagrange-SQP methods
........... 24
2.6
Mesh-independence
............................. 26
2.6.1
Approximation of the infinite dimensional algorithm
....... 27
2.6.2
Convergence results for Algorithm
2.6............... 30
2.6.3
Convergence results for Algorithm
2.7............... 33
2.6.4
Asymptotic mesh-independence
.................. 35
2.6.5
Strong mesh-independence
..................... 36
2.7
Applications
................................. 36
2.7.1
Optimal control problems for the Burgers equation
....... 36
2.7.2
Optimal control of a phase-field model
.............. 52
2.7.3
Parameter identification problems
................. 56
2.8
Lagrange-Newton-SQP and generalized Newton s method
........ 59
2.8.1
The optimal control problem
.................... 60
2.8.2
The Lagrange-Newton-SQP method
................ 64
2.8.3
Generalized equation and Newton s method
........... 65
2.8.4
Strong regularity
.......................: . . 66
2.8.5
The linear-quadratic optimal control problem
.......... 68
2.8.6
The primal-dual active set algorithm
............... 70
3
Suboptimal
control using POD
72
3.1
Introduction
................................. 72
3.2
Proper orthogonal decomposition (POD)
................. 74
3.2.1
Abstract dynamical system
.................... 74
3.2.2
Computation of the POD basis
.................. 75
3.3
POD and singular value decomposition
.................. 79
3.4
Error estimates for
semilinear
problems
.................. 83
3.4.1
Equations with locally Lipschitz-continuous nonlinearity
.... 83
3.4.2
Error estimates for a model describing the laser hardening of steel
85
3.5
Error estimates for a general equation in fluid dynamics
......... 88
3.5.1 Case X
=
V
............................. 89
3.5.2
Case X
=
Я
............................. 94
3.6
Applications
................................. 94
3.6.1
Optimal control of the Burgers equation
............. 94
3.6.2
Optimal control of
a phase-fíeld
model
.............. 99
3.6.3
Nonlinear boundary control of a heat equation
.......... 99
3.6.4
Control of laser surface hardening
................. 103
3.6.5
Numerical experiments for the control of laser surface hardening
106
3.6.6
Numerical solution of the state equations
............. 110
|
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| id | DE-604.BV013699924 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:50:29Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009362743 |
| oclc_num | 634766186 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-703 |
| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-703 |
| physical | VI, 131 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Fachbibl. für Mathematik, Univ. |
| record_format | marc |
| series | Grazer mathematische Berichte |
| series2 | Grazer mathematische Berichte |
| spelling | Volkwein, Stefan 1966- Verfasser (DE-588)118138529 aut Optimal and suboptimal control of partial differential equations augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition Stefan Volkwein Graz Fachbibl. für Mathematik, Univ. 2001 VI, 131 S. txt rdacontent n rdamedia nc rdacarrier Grazer mathematische Berichte 343 Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Sequenzielle quadratische Optimierung (DE-588)4451045-7 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Sequenzielle quadratische Optimierung (DE-588)4451045-7 s Grazer mathematische Berichte 343 (DE-604)BV008016881 343 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009362743&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Volkwein, Stefan 1966- Optimal and suboptimal control of partial differential equations augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition Grazer mathematische Berichte Partielle Differentialgleichung (DE-588)4044779-0 gnd Sequenzielle quadratische Optimierung (DE-588)4451045-7 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4451045-7 (DE-588)4121428-6 |
| title | Optimal and suboptimal control of partial differential equations augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition |
| title_auth | Optimal and suboptimal control of partial differential equations augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition |
| title_exact_search | Optimal and suboptimal control of partial differential equations augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition |
| title_full | Optimal and suboptimal control of partial differential equations augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition Stefan Volkwein |
| title_fullStr | Optimal and suboptimal control of partial differential equations augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition Stefan Volkwein |
| title_full_unstemmed | Optimal and suboptimal control of partial differential equations augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition Stefan Volkwein |
| title_short | Optimal and suboptimal control of partial differential equations |
| title_sort | optimal and suboptimal control of partial differential equations augmented lagrange sqp methods and reduced order modeling with proper orthogonal decomposition |
| title_sub | augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition |
| topic | Partielle Differentialgleichung (DE-588)4044779-0 gnd Sequenzielle quadratische Optimierung (DE-588)4451045-7 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Partielle Differentialgleichung Sequenzielle quadratische Optimierung Optimale Kontrolle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009362743&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008016881 |
| work_keys_str_mv | AT volkweinstefan optimalandsuboptimalcontrolofpartialdifferentialequationsaugmentedlagrangesqpmethodsandreducedordermodelingwithproperorthogonaldecomposition |