A theory of optimization and optimal control for nonlinear evolution and singular equations: applications to nonlinear partial differential equations
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore u.a.
World Scientific Publ.
1990
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 274 S. |
| ISBN: | 9810203268 |
Staff View
MARC
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| 245 | 1 | 0 | |a A theory of optimization and optimal control for nonlinear evolution and singular equations |b applications to nonlinear partial differential equations |c Mieczyslaw Altman |
| 264 | 1 | |a Singapore u.a. |b World Scientific Publ. |c 1990 | |
| 300 | |a XVII, 274 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Banach spaces | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Evolution equations, Nonlinear | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Operator equations | |
| 650 | 0 | 7 | |a Nichtlineare Evolutionsgleichung |0 (DE-588)4221363-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare singuläre Integralgleichung |0 (DE-588)4171758-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare singuläre Integralgleichung |0 (DE-588)4171758-2 |D s |
| 689 | 0 | 1 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |D s |
| 689 | 0 | |5 DE-604 | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PREFACE vii
Chapter 1 A MAXIMAL ELEMENT PRINCIPLE FOR CONSTRAINT SETS 1
1. A Maximal Element Principle 1
2. The Dubovitskii Milyutin Extremum Principle 3
3. A General Local Maximum Principle for Optimal
Control 6
Chapter 2 OPTIMIZATION AND OPTIMAL CONTROL OF NONLINEAR
EVOLUTION EQUATIONS VIA GLIM I 11
1. Nonlinear Evolution Equations as Constraints 11
2. Solving Nonlinear Evolution Equations Via
GLIM I 12
3. GLIM la 18
4. Smoothing Operators and Elliptic Regularization 21
5. Elliptic Regularization 31
6. An Application of the Theory of Co Semigroups 33
7. Existence of Tangent Directions 34
8. Solving Nonlinear Evolution Equations Involving
Control Functions 36
9. Smoothing Operators Combined with Elliptic
Regularization 40
10. Elliptic Regularization 44
11. Existence of Tangent Directions 47
Chapter 3 OPTIMIZATION AND OPTIMAL CONTROL OF NONLINEAR
EVOLUTION EQUATIONS VIA GLIM II 50
1. Solving Nonlinear Evolution Equations via
GLIM II 50
2. Solving Nonlinear Evolution Equations via
GLIM IIa 55
3. Smoothing Operators Combined with Elliptic
Regularization 58
4. Elliptic Regularization 60
5. Existence of Tangent Directions via GLIM II, Ila 61
6. Solving Nonlinear Evolution Equations Involving
Control Functions 62
xiii
Contents
7. Smoothing Operators Combined with Elliptic
Regularization 66
8. Elliptic Regularization 67
9. Existence of Tangent Directions 68
Chapter 4 OPTIMIZATION AND OPTIMAL CONTROL OF NONLINEAR
EVOLUTION EQUATIONS VIA GLIM III 71
1. Solving Nonlinear Evolution Equations via
GLIM III 71
2. GLIM Ilia 77
3. Smoothing Operators and Elliptic Regularization 79
4. Elliptic Regularization and Convex Approximate
Linearization 85
5. Existence of Tangent Directions via GLIM III
and GLIM Ilia 87
6. Solving Nonlinear Evolution Equations Involving
Control Functions 89
7. Smoothing Operators and Elliptic Regularization 95
8. Elliptic Regularization without Smoothing
Operators 98
9. Tangent Directions involving Control Functions 101
10. A Local Maximum Principle for Optimal Control 102
Chapter 5 SMOOTHING OPERATORS WITHOUT ELLIPTIC REGULARIZATION
FOR NONLINEAR EVOLUTION EQUATIONS 107
1. Solving Nonliner Evolution Equations via GLIM Ib 108
2. GLIM IIb 110
3. GLIM IIIb 110
4. Smoothing Operators and GLIM Ib 113
5. Smoothing Operators and GLIM IIb 117
6. Smoothing Operators and GLIM IIIb 117
Chapter 6 OPTIMIZATION AND OPTIMAL CONTROL OF NONLINEAR
SINGULAR EQUATIONS VIA GLIM 1 120
1. Solving Nonlinear Singular Equations via GLIM I 120
2. GLIM Ia for Nonlinear Singular Equations 125
3. Smoothing Operators Combined with Elliptic
Regularization 127
4. Elliptic Regularization 132
5. Existence of Tangent Directions 134
6. Nonlinear Singular Equations Involving Control
Functions 136
7. Smoothing Operators Combined with Elliptic
xiv
Contents
Regularization 140
8. Elliptic Regularization 143
9. Existence of Tangent Directions 146
Chapter 7 OPTIMIZATION AND OPTIMAL CONTROL OF NONLINEAR
SINGULAR EQUATIONS VIA GLIM II 148
1. Solving Nonlinear Singular Equations via
GLIM II 148
2. Solving Nonlinear Singular Equations via
GLIM IIa 152
3. Smoothing Operators Combined with Elliptic
Regularization for Nonlinear Singular
Equations 154
4. Elliptic Regularization 156
5. Existence of Tangent Directions 157
6. Nonlinear Singular Equations Involving Control
Functions 158
7. Smoothing Operators Combined with Elliptic
Regularization 162
8. Elliptic Regularization 163
9. Tangent Directions via GLIM II 164
Chapter 8 OPTIMIZATION AND OPTIMAL CONTROL OF NONLINEAR
SINGULAR EQUATIONS VIA GLIM III 166
1. GLIM III 166
2. GLIM IIIa 170
3. Smoothing Operators Combined with Elliptic
Regularization 172
4. Elliptic Regularization 174
5. Existence of Tangent Directions via GLIM III
and GLIM IIIa for Nonlinear Singular Equations 176
6. Solving Nonlinear Singular Equations Involving
Control Functions 177
7. Smoothing Operators and Elliptic Regularization
for Nonlinear Singular Equations 182
8. Elliptic Regularization without Smoothing
Operators for Nonlinear Singular Equations 185
9. Tangent Directions for Optimal Control of
Nonlinear Singular Equations 188
Chapter 9 SMOOTHING OPERATORS WITHOUT ELLIPTIC REGULARIZATION
FOR NONLINEAR SINGULAR EQUATIONS 190
1. Nonlinear Singular Equations via GLIM Ib 190
XV
Contents
2. GLIM IIb 191
3. GLIM IIIb 191
4. Smoothing Operators and GLIM Ib 192
5. Smoothing Operators and GLIM IIb 193
6. Smoothing Operators and GLIM IIIb 193
Chapter 10 AN EXTREMUM PRINCIPLE FOR OPTIMAL CONTROL OF NONLINEAR
SINGULAR EQUATIONS AND SMOOTH CONVEX PROBLEMS 195
1. The Euler Lagrange Equation 195
2. An Extremum Principle 198
Chapter 11 APPLICATIONS 202
1. Applications of Optimal Control of Nonlinear
Evolution Equations 202
2. Optimal Control of the Quasilinear Korteweg
de Vries Equation 214
2a. Optimal Control of Nonlinear Korteweg de Vries
Equation 217
3. Applications of Optimal Control of Nonlinear
Singular Equations 220
4. Optimal Control of Nonlinear Systems of
Partial Differential Equations 226
5. Optimal Control of Linear Equations with Small
Nonlinear Perturbations 229
6. The Case of Lx x x, + oxt x 233
Chapter 12 OPTIMIZATION AND OPTIMAL CONTROL OF NONLINEAR
EVOLUTION AND SINGULAR EQUATIONS IN ARBITRARY
BANACH SPACES 236
1. Nonlinear Evolution Equations in Abritrary
Banach Spaces 237
2. Existence of Tangent Directions for Nonlinear
Evolution Equations in Arbitrary Banach Spaces 243
3. Nonlinear Evolution Equations Involving Control
Functions 245
4. Tangent Directions for Controlled Nonlinear
Evolution Equations in Arbitrary Banach Spaces 249
5. Nonlinear Singular Operator Equations 251
6. Existence of Tangent Directions for Nonlinear
Singular Equations in Arbitrary Banach Spaces 256
7. Nonlinear Singular Equations Involving Controls 257
8. Tangent Directions for Controlled Nonlinear
Singular Equations in Arbitrary Banach Spaces 260
xvi
Contents
Appendix A DIRECT APPROACH TO OPTIMAL CONTROL WITH MIXED
CONSTRAINTS 263
1. The Kuhn Tucker Theorem for Nonlinear Evolution
Equations in Banach Spaces 263
2. The Kuhn Tucker Theorem for Nonlinear Singular
Equations in Banach Spaces 265
3. An Extremum Principle for Smooth Convex Control
Problems 267
4. Optimal Control with Nondifferentiable Objective
Functional 269
5. Optimal Control with Nondifferentiable Objective
Functional and Equality Constraint 271
References 272
Index 274
xvii
|
| any_adam_object | 1 |
| author | Altman, Mieczyslaw 1916-1997 |
| author_GND | (DE-588)1063754143 |
| author_facet | Altman, Mieczyslaw 1916-1997 |
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| ctrlnum | (OCoLC)22832056 (DE-599)BVBBV006590424 |
| 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 |
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| id | DE-604.BV006590424 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:48:50Z |
| institution | BVB |
| isbn | 9810203268 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004207383 |
| oclc_num | 22832056 |
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| owner | DE-739 DE-703 DE-706 DE-634 DE-11 DE-188 |
| owner_facet | DE-739 DE-703 DE-706 DE-634 DE-11 DE-188 |
| physical | XVII, 274 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | World Scientific Publ. |
| record_format | marc |
| spelling | Altman, Mieczyslaw 1916-1997 Verfasser (DE-588)1063754143 aut A theory of optimization and optimal control for nonlinear evolution and singular equations applications to nonlinear partial differential equations Mieczyslaw Altman Singapore u.a. World Scientific Publ. 1990 XVII, 274 S. txt rdacontent n rdamedia nc rdacarrier Banach spaces Differential equations, Partial Evolution equations, Nonlinear Mathematical optimization Operator equations Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd rswk-swf Nichtlineare singuläre Integralgleichung (DE-588)4171758-2 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Nichtlineare singuläre Integralgleichung (DE-588)4171758-2 s Optimale Kontrolle (DE-588)4121428-6 s DE-604 Nichtlineare Evolutionsgleichung (DE-588)4221363-0 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004207383&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Altman, Mieczyslaw 1916-1997 A theory of optimization and optimal control for nonlinear evolution and singular equations applications to nonlinear partial differential equations Banach spaces Differential equations, Partial Evolution equations, Nonlinear Mathematical optimization Operator equations Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd Nichtlineare singuläre Integralgleichung (DE-588)4171758-2 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4221363-0 (DE-588)4171758-2 (DE-588)4121428-6 |
| title | A theory of optimization and optimal control for nonlinear evolution and singular equations applications to nonlinear partial differential equations |
| title_auth | A theory of optimization and optimal control for nonlinear evolution and singular equations applications to nonlinear partial differential equations |
| title_exact_search | A theory of optimization and optimal control for nonlinear evolution and singular equations applications to nonlinear partial differential equations |
| title_full | A theory of optimization and optimal control for nonlinear evolution and singular equations applications to nonlinear partial differential equations Mieczyslaw Altman |
| title_fullStr | A theory of optimization and optimal control for nonlinear evolution and singular equations applications to nonlinear partial differential equations Mieczyslaw Altman |
| title_full_unstemmed | A theory of optimization and optimal control for nonlinear evolution and singular equations applications to nonlinear partial differential equations Mieczyslaw Altman |
| title_short | A theory of optimization and optimal control for nonlinear evolution and singular equations |
| title_sort | a theory of optimization and optimal control for nonlinear evolution and singular equations applications to nonlinear partial differential equations |
| title_sub | applications to nonlinear partial differential equations |
| topic | Banach spaces Differential equations, Partial Evolution equations, Nonlinear Mathematical optimization Operator equations Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd Nichtlineare singuläre Integralgleichung (DE-588)4171758-2 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Banach spaces Differential equations, Partial Evolution equations, Nonlinear Mathematical optimization Operator equations Nichtlineare Evolutionsgleichung Nichtlineare singuläre Integralgleichung Optimale Kontrolle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004207383&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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