Optimization with PDE constraints:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer
2009
|
| Schriftenreihe: | Mathematical modelling
23 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 270 S. Ill., graph. Darst. |
| ISBN: | 9781402088384 |
Internformat
MARC
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| 245 | 1 | 0 | |a Optimization with PDE constraints |c M. Hinze ; R. Pinnau ; M. Ulbrich ; S. Ulbrich |
| 264 | 1 | |a Dordrecht |b Springer |c 2009 | |
| 300 | |a XI, 270 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical modelling |v 23 | |
| 650 | 7 | |a Optimisation mathématique |2 ram | |
| 650 | 7 | |a Équations aux dérivées partielles |2 ram | |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare Optimierung |0 (DE-588)4128192-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nebenbedingung |0 (DE-588)4140066-5 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Hinze, Michael |e Sonstige |4 oth | |
| 700 | 1 | |a Pinnau, René |d 1971- |e Sonstige |0 (DE-588)121101827 |4 oth | |
| 700 | 1 | |a Ulbrich, Michael |e Sonstige |4 oth | |
| 700 | 1 | |a Ulbrich, Stefan |e Sonstige |4 oth | |
| 830 | 0 | |a Mathematical modelling |v 23 |w (DE-604)BV011613239 |9 23 | |
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Datensatz im Suchindex
| _version_ | 1804138364324020224 |
|---|---|
| adam_text | Contents
Preface
v
1
Analytical Background and Optimality Theory
............ 1
Stefan Ulbrich
............................... 1
1.1
Introduction and Examples
..................... 1
1.1.1
Introduction
......................... 1
1.1.2
Examples for Optimization Problems with PDEs
...... 4
1.1.3
Optimization of a Stationary Heating Process
........ 5
1.1.4
Optimization of an Unsteady Heating Processes
...... 7
1.1.5
Optimal Design
....................... 8
1.2
Linear Functional Analysis and Sobolev Spaces
.......... 9
1.2.1
Banach and Hubert Spaces
................. 10
1.2.2
Sobolev Spaces
....................... 13
1.2.3
Weak Convergence
..................... 24
1.3
Weak Solutions of Elliptic and Parabolic PDEs
........... 26
1.3.1
Weak Solutions of Elliptic PDEs
.............. 26
1.3.2
Weak Solutions of Parabolic PDEs
............. 36
1.4
Gâteaux-
and
Freenet
Differentiability
............... 50
1.4.1
Basic Definitions
....................... 50
1.4.2
Implicit Function Theorem
................. 52
1.5
Existence of Optimal Controls
.................... 52
1.5.1
Existence Result for a General Linear-Quadratic
Problem
........................... 52
1.5.2
Existence Results for Nonlinear Problems
......... 54
1.5.3
Applications
......................... 56
1.6
Reduced Problem, Sensitivities and
Adjoints
............ 57
1.6.1
Sensitivity Approach
..................... 58
1.6.2
Adjoint Approach
...................... 59
1.6.3
Application to a Linear-Quadratic Optimal Control
Problem
........................... 60
1.6.4
A Lagrangian-Based View of the Adjoint Approach
.... 63
їх
Contents
1.6.5
Second
Derivatives ..................... 64
1.7 Optimality
Conditions
........................ 65
1.7.1 Optimality
Conditions
for Simply Constrained Problems
. . 65
1.7.2
Optimality Conditions for Control-Constrained
Problems
........................... 70
1.7.3
Optimality Conditions for Problems with General
Constraints
.......................... 80
1.8
Optimal Control of Instationary Incompressible Navier-Stokes
Flow
................................. 88
1.8.1
Functional Analytic Setting
................. 89
1.8.2
Analysis of the Flow Control Problem
........... 91
1.8.3
Reduced Optimal Control Problem
............. 94
Optimization Methods in Banach Spaces
................ 97
Michael Ulbrich
.............................. 97
2.1
Synopsis
............................... 97
2.2
Globally Convergent Methods in Banach Spaces
.......... 99
2.2.1
Unconstrained Optimization
................. 99
2.2.2
Optimization on Closed Convex Sets
............ 104
2.2.3
General Optimization Problems
............... 109
2.3
Newton-Based Methods
—
A Preview
................ 109
2.3.1
Unconstrained Problems
—
Newton s Method
........ 109
2.3.2
Simple Constraints
...................... 110
2.3.3
General Inequality Constraints
............... 113
2.4
Generalized Newton Methods
.................... 115
2.4.1
Motivation: Application to Optimal Control
........ 115
2.4.2
A General
Superlinear
Convergence Result
......... 116
2.4.3
The Classical Newton s Method
............... 119
2.4.4
Generalized Differential and Semismoothness
....... 120
2.4.5
Semismooth Newton Methods
................ 123
2.5
Semismooth Newton Methods in Function Spaces
......... 125
2.5.1
Pointwise Bound Constraints in L2
............. 125
2.5.2
Semismoothness of Superposition Operators
........ 126
2.5.3
Pointwise Bound Constraints in L2 Revisited
........ 129
2.5.4
Application to Optimal Control
............... 130
2.5.5
General Optimization Problems with Inequality
Constraints in L2
...................... 132
2.5.6
Application to Elliptic Optimal Control Problems
..... 133
2.5.7
Optimal Control of the Incompressible Navier-Stokes
Equations
.......................... 137
2.6
Sequential Quadratic Programming
................. 140
2.6.1
Lagrange-Newton Methods for Equality Constrained
Problems
........................... 140
2.6.2
The Josephy-Newton Method
................ 144
2.6.3
SQP Methods for Inequality Constrained Problems
..... 148
Contents xj
2.7
State-Constrained
Problems.....................151
2.7.1 SQP
Methods
........................152
2.7.2 Semismooth Newton
Methods
................152
2.8
Further Aspects
...........................155
2.8.1
Mesh Independence.....................
155
2.8.2 Application
of Fast Solvers
.................156
2.8.3
Other Methods
........................156
3
Discrete Concepts in PDE Constrained Optimization
.........157
Michael
Hinze...............................157
3.1
Introduction
.............................157
3.2
Control Constraints
.........................158
3.2.1
Stationary Model Problem
.................. 158
3.2.2
First Discretize, Then Optimize
............... 160
3.2.3
First Optimize, Then Discretize
............... 161
3.2.4
Discussion and Implications
................. 163
3.2.5
The Variational Discretization Concept
........... 164
3.2.6
Error Estimates
....................... 167
3.2.7
Boundary Control
...................... 177
3.2.8
Some Literature Related to Control Constraints
....... 1%
3.3
Constraints on the State
....................... 197
3.3.1
Pointwise Bounds on the State
...............198
3.3.2
Pointwise Bounds on the Gradient of the State
.......219
3.4
Time Dependent Problem
......................227
3.4.1
Mathematical Model, State Equation
............227
3.4.2
Optimization Problem
....................229
3.4.3
Discretization
........................229
3.4.4
Further Literature on Control of Time-Dependent
Problems
...........................231
4
Applications
................................233
RenéPinnau
................................233
4.1
Optimal Semiconductor Design
...................233
4.1.1
Semiconductor Device Physics
............... 234
4.1.2
The Optimization Problem
................. 240
4.1.3
Numerical Results
...................... 246
4.2
Optimal Control of Glass Cooling
.................. 250
4.2.1
Modeling
...........................
251
4.2.2
Optimal Boundary Control
.................254
4.2.3
Numerical Results
......................260
References
...................................265
|
| adam_txt |
Contents
Preface
v
1
Analytical Background and Optimality Theory
. 1
Stefan Ulbrich
. 1
1.1
Introduction and Examples
. 1
1.1.1
Introduction
. 1
1.1.2
Examples for Optimization Problems with PDEs
. 4
1.1.3
Optimization of a Stationary Heating Process
. 5
1.1.4
Optimization of an Unsteady Heating Processes
. 7
1.1.5
Optimal Design
. 8
1.2
Linear Functional Analysis and Sobolev Spaces
. 9
1.2.1
Banach and Hubert Spaces
. 10
1.2.2
Sobolev Spaces
. 13
1.2.3
Weak Convergence
. 24
1.3
Weak Solutions of Elliptic and Parabolic PDEs
. 26
1.3.1
Weak Solutions of Elliptic PDEs
. 26
1.3.2
Weak Solutions of Parabolic PDEs
. 36
1.4
Gâteaux-
and
Freenet
Differentiability
. 50
1.4.1
Basic Definitions
. 50
1.4.2
Implicit Function Theorem
. 52
1.5
Existence of Optimal Controls
. 52
1.5.1
Existence Result for a General Linear-Quadratic
Problem
. 52
1.5.2
Existence Results for Nonlinear Problems
. 54
1.5.3
Applications
. 56
1.6
Reduced Problem, Sensitivities and
Adjoints
. 57
1.6.1
Sensitivity Approach
. 58
1.6.2
Adjoint Approach
. 59
1.6.3
Application to a Linear-Quadratic Optimal Control
Problem
. 60
1.6.4
A Lagrangian-Based View of the Adjoint Approach
. 63
їх
Contents
1.6.5
Second
Derivatives . 64
1.7 Optimality
Conditions
. 65
1.7.1 Optimality
Conditions
for Simply Constrained Problems
. . 65
1.7.2
Optimality Conditions for Control-Constrained
Problems
. 70
1.7.3
Optimality Conditions for Problems with General
Constraints
. 80
1.8
Optimal Control of Instationary Incompressible Navier-Stokes
Flow
. 88
1.8.1
Functional Analytic Setting
. 89
1.8.2
Analysis of the Flow Control Problem
. 91
1.8.3
Reduced Optimal Control Problem
. 94
Optimization Methods in Banach Spaces
. 97
Michael Ulbrich
. 97
2.1
Synopsis
. 97
2.2
Globally Convergent Methods in Banach Spaces
. 99
2.2.1
Unconstrained Optimization
. 99
2.2.2
Optimization on Closed Convex Sets
. 104
2.2.3
General Optimization Problems
. 109
2.3
Newton-Based Methods
—
A Preview
. 109
2.3.1
Unconstrained Problems
—
Newton's Method
. 109
2.3.2
Simple Constraints
. 110
2.3.3
General Inequality Constraints
. 113
2.4
Generalized Newton Methods
. 115
2.4.1
Motivation: Application to Optimal Control
. 115
2.4.2
A General
Superlinear
Convergence Result
. 116
2.4.3
The Classical Newton's Method
. 119
2.4.4
Generalized Differential and Semismoothness
. 120
2.4.5
Semismooth Newton Methods
. 123
2.5
Semismooth Newton Methods in Function Spaces
. 125
2.5.1
Pointwise Bound Constraints in L2
. 125
2.5.2
Semismoothness of Superposition Operators
. 126
2.5.3
Pointwise Bound Constraints in L2 Revisited
. 129
2.5.4
Application to Optimal Control
. 130
2.5.5
General Optimization Problems with Inequality
Constraints in L2
. 132
2.5.6
Application to Elliptic Optimal Control Problems
. 133
2.5.7
Optimal Control of the Incompressible Navier-Stokes
Equations
. 137
2.6
Sequential Quadratic Programming
. 140
2.6.1
Lagrange-Newton Methods for Equality Constrained
Problems
. 140
2.6.2
The Josephy-Newton Method
. 144
2.6.3
SQP Methods for Inequality Constrained Problems
. 148
Contents xj
2.7
State-Constrained
Problems.151
2.7.1 SQP
Methods
.152
2.7.2 Semismooth Newton
Methods
.152
2.8
Further Aspects
.155
2.8.1
Mesh Independence.
155
2.8.2 Application
of Fast Solvers
.156
2.8.3
Other Methods
.156
3
Discrete Concepts in PDE Constrained Optimization
.157
Michael
Hinze.157
3.1
Introduction
.157
3.2
Control Constraints
.158
3.2.1
Stationary Model Problem
. 158
3.2.2
First Discretize, Then Optimize
. 160
3.2.3
First Optimize, Then Discretize
. 161
3.2.4
Discussion and Implications
. 163
3.2.5
The Variational Discretization Concept
. 164
3.2.6
Error Estimates
. 167
3.2.7
Boundary Control
. 177
3.2.8
Some Literature Related to Control Constraints
. 1%
3.3
Constraints on the State
. 197
3.3.1
Pointwise Bounds on the State
.198
3.3.2
Pointwise Bounds on the Gradient of the State
.219
3.4
Time Dependent Problem
.227
3.4.1
Mathematical Model, State Equation
.227
3.4.2
Optimization Problem
.229
3.4.3
Discretization
.229
3.4.4
Further Literature on Control of Time-Dependent
Problems
.231
4
Applications
.233
RenéPinnau
.233
4.1
Optimal Semiconductor Design
.233
4.1.1
Semiconductor Device Physics
. 234
4.1.2
The Optimization Problem
. 240
4.1.3
Numerical Results
. 246
4.2
Optimal Control of Glass Cooling
. 250
4.2.1
Modeling
.
251
4.2.2
Optimal Boundary Control
.254
4.2.3
Numerical Results
.260
References
.265 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author_GND | (DE-588)121101827 |
| building | Verbundindex |
| bvnumber | BV035187742 |
| classification_rvk | SK 540 SK 660 |
| classification_tum | MAT 460f MAT 916f MAT 350f |
| ctrlnum | (OCoLC)494855123 (DE-599)DNB98908101X |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV035187742 |
| illustrated | Illustrated |
| index_date | 2024-07-02T23:00:29Z |
| indexdate | 2024-07-09T21:27:01Z |
| institution | BVB |
| isbn | 9781402088384 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016994402 |
| oclc_num | 494855123 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-355 DE-BY-UBR DE-706 DE-20 DE-91G DE-BY-TUM DE-29T DE-83 DE-11 DE-188 |
| owner_facet | DE-384 DE-703 DE-355 DE-BY-UBR DE-706 DE-20 DE-91G DE-BY-TUM DE-29T DE-83 DE-11 DE-188 |
| physical | XI, 270 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Mathematical modelling |
| series2 | Mathematical modelling |
| spelling | Optimization with PDE constraints M. Hinze ; R. Pinnau ; M. Ulbrich ; S. Ulbrich Dordrecht Springer 2009 XI, 270 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical modelling 23 Optimisation mathématique ram Équations aux dérivées partielles ram Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Nebenbedingung (DE-588)4140066-5 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 s Nebenbedingung (DE-588)4140066-5 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Hinze, Michael Sonstige oth Pinnau, René 1971- Sonstige (DE-588)121101827 oth Ulbrich, Michael Sonstige oth Ulbrich, Stefan Sonstige oth Mathematical modelling 23 (DE-604)BV011613239 23 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016994402&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Optimization with PDE constraints Mathematical modelling Optimisation mathématique ram Équations aux dérivées partielles ram Partielle Differentialgleichung (DE-588)4044779-0 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd Nebenbedingung (DE-588)4140066-5 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4128192-5 (DE-588)4140066-5 |
| title | Optimization with PDE constraints |
| title_auth | Optimization with PDE constraints |
| title_exact_search | Optimization with PDE constraints |
| title_exact_search_txtP | Optimization with PDE constraints |
| title_full | Optimization with PDE constraints M. Hinze ; R. Pinnau ; M. Ulbrich ; S. Ulbrich |
| title_fullStr | Optimization with PDE constraints M. Hinze ; R. Pinnau ; M. Ulbrich ; S. Ulbrich |
| title_full_unstemmed | Optimization with PDE constraints M. Hinze ; R. Pinnau ; M. Ulbrich ; S. Ulbrich |
| title_short | Optimization with PDE constraints |
| title_sort | optimization with pde constraints |
| topic | Optimisation mathématique ram Équations aux dérivées partielles ram Partielle Differentialgleichung (DE-588)4044779-0 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd Nebenbedingung (DE-588)4140066-5 gnd |
| topic_facet | Optimisation mathématique Équations aux dérivées partielles Partielle Differentialgleichung Nichtlineare Optimierung Nebenbedingung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016994402&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011613239 |
| work_keys_str_mv | AT hinzemichael optimizationwithpdeconstraints AT pinnaurene optimizationwithpdeconstraints AT ulbrichmichael optimizationwithpdeconstraints AT ulbrichstefan optimizationwithpdeconstraints |