Theory of suboptimal decisions: decomposition and aggregation
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1988
|
| Series: | Mathematics and its applications / Soviet series
12 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 384 S. |
| ISBN: | 9027724016 |
Staff View
MARC
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| 240 | 1 | 0 | |a Dekompozicija, agregirovanie i približennaja optizacija |
| 245 | 1 | 0 | |a Theory of suboptimal decisions |b decomposition and aggregation |c A. A. Pervozvanskii and V. G. Gaitsgori |
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Record in the Search Index
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| adam_text | Table of Contents
Preface xi
Introduction xv
Chapter 1: The Perturbation Method in Mathematical Programming 1
1.1. Formulation and peculiarities of problems 2
1.2. Perturbations in linear programs 11
1.3 Nonlinear programs: perturbations in objective functions 25
1.4. Necessary and sufficient conditions for an extremum. 36
Quasiconvex and quasilinear programs
1.5. Perturbations in nonconvex programs 52
Chapter 2: Approximate Decomposition and Aggregation for 65
Finite Dimensional Deterministic Problems
2.1. Perturbed decomposable structures and two level planning 67
2.2. Aggregation of activities 75
2.3 Weakly controllable input output characteristics 87
2.4. Input output analysis 95
2.5. Aggregation in optimization models based on 106
input output analysis
2.6. Aggregation in the interregional transportation problem 114
with regard to price scales
2.7. Optimization of discrete dynamic systems 122
2.8. Control of weakly dynamic systems under 130
state variable constraints
Chapter 3: Singular Programs 136
3.1. Singularity and regularization in quasiconvex problems 137
3.2. The auxiliary problem in the singular case 144
3.3. An approximate aggregation of Markov chains with incomes 151
3.4. An approximation algorithm for Markov programming 160
x Theory of Suboptimal Decisions: Decomposition and Aggregation
3.5. An iterative algorithm for suboptimization 166
3.6. An artificial introduction of singular perturbations 178
in compact inverse methods
Chapter 4: The Perturbation Method in Stochastic Programming 186
4.1. One and two stage problems 187
4.2. Optimal control problems with small random perturbations 193
4.3. Discrete dynamic systems with weak or aggregatable controls. 209
An asymptotic stochastic maximum principle
4.4. Sliding planning and suboptimal decomposition of operative 216
control in a production system
4.5. Sliding planning on an infinite horizon 222
4.6. Control of weakly dynamic systems under random disturbances 228
Chapter 5: Suboptimal Linear Regulator Design 233
5.1. The LQ problem. Suboptimal decomposition 235
5.2. Loss of controllability, singularity, and suboptimal aggregation 250
5.3. Examples of suboptimal regulator synthesis 268
5.4. Control of oscillatory systems 276
5.5. LQG problems 291
Chapter 6: Nonlinear Optimal Control Problems 306
6.1. The maximum principle and smooth solutions 307
6.2. The general terminal problem 322
6.3. Difference approximations 329
6.4. Weak control (nonuniqueness of the reduced solution) 339
6.5. Aggregation in a singular perturbed problem 354
Related Literature 369
Index 381
|
| any_adam_object | 1 |
| author | Pervozvanskij, Anatolij Arkadʹevič Gajcgori, Vladimir G. |
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| author_sort | Pervozvanskij, Anatolij Arkadʹevič |
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| bvnumber | BV001993962 |
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| discipline | Mathematik |
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| id | DE-604.BV001993962 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:38:33Z |
| institution | BVB |
| isbn | 9027724016 |
| language | English |
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| physical | XVII, 384 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
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| publisher | Kluwer |
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| series2 | Mathematics and its applications / Soviet series |
| spelling | Pervozvanskij, Anatolij Arkadʹevič Verfasser (DE-588)171755413 aut Dekompozicija, agregirovanie i približennaja optizacija Theory of suboptimal decisions decomposition and aggregation A. A. Pervozvanskii and V. G. Gaitsgori Dordrecht [u.a.] Kluwer 1988 XVII, 384 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 12 Optimierung (DE-588)4043664-0 gnd rswk-swf Störungstheorie (DE-588)4128420-3 gnd rswk-swf Dekomposition (DE-588)4149030-7 gnd rswk-swf Aggregation (DE-588)4000728-5 gnd rswk-swf Störungstheorie (DE-588)4128420-3 s Optimierung (DE-588)4043664-0 s DE-604 Dekomposition (DE-588)4149030-7 s Aggregation (DE-588)4000728-5 s Gajcgori, Vladimir G. Verfasser aut Soviet series Mathematics and its applications 12 (DE-604)BV004708148 12 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001300700&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pervozvanskij, Anatolij Arkadʹevič Gajcgori, Vladimir G. Theory of suboptimal decisions decomposition and aggregation Optimierung (DE-588)4043664-0 gnd Störungstheorie (DE-588)4128420-3 gnd Dekomposition (DE-588)4149030-7 gnd Aggregation (DE-588)4000728-5 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4128420-3 (DE-588)4149030-7 (DE-588)4000728-5 |
| title | Theory of suboptimal decisions decomposition and aggregation |
| title_alt | Dekompozicija, agregirovanie i približennaja optizacija |
| title_auth | Theory of suboptimal decisions decomposition and aggregation |
| title_exact_search | Theory of suboptimal decisions decomposition and aggregation |
| title_full | Theory of suboptimal decisions decomposition and aggregation A. A. Pervozvanskii and V. G. Gaitsgori |
| title_fullStr | Theory of suboptimal decisions decomposition and aggregation A. A. Pervozvanskii and V. G. Gaitsgori |
| title_full_unstemmed | Theory of suboptimal decisions decomposition and aggregation A. A. Pervozvanskii and V. G. Gaitsgori |
| title_short | Theory of suboptimal decisions |
| title_sort | theory of suboptimal decisions decomposition and aggregation |
| title_sub | decomposition and aggregation |
| topic | Optimierung (DE-588)4043664-0 gnd Störungstheorie (DE-588)4128420-3 gnd Dekomposition (DE-588)4149030-7 gnd Aggregation (DE-588)4000728-5 gnd |
| topic_facet | Optimierung Störungstheorie Dekomposition Aggregation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001300700&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004708148 |
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