Introductory optimization dynamics: optimal control with economics and management applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1991
|
| Edition: | 2., revised and enl. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 474 S. graph. Darst. |
| ISBN: | 3540544623 0387544623 |
Staff View
MARC
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| 100 | 1 | |a Tu, Pierre N. V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introductory optimization dynamics |b optimal control with economics and management applications |c Pierre N. V. Tu |
| 250 | |a 2., revised and enl. ed. | ||
| 264 | 1 | |a Berlin u.a. |b Springer |c 1991 | |
| 300 | |a XVI, 474 S. |b graph. Darst. | ||
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| 650 | 4 | |a Optimisation mathématique | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Mathematical optimization | |
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Record in the Search Index
| _version_ | 1804118676154089472 |
|---|---|
| adam_text | Pierre N V Tu
Introductory
Optimization Dynamics
Optimal Control with Economics and
Management Applications
Second, Revised and Enlarged Edition
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
Hong Kong Barcelona
Budapest
CONTENTS
Preface
Chapter 1
Chapter 2
Page
INTRODUCTION 1
The Dynamic Optimization Problem 1
The Control Problem 1
The State of the Dynamic System 2
The Control Variables 3
Reachability, Controllability and Observability 3
The Objective Functional 4
Some Examples 5
The Calculus of Variations and Optimal Control
Problems 6
THE CALCULUS OF VARIATIONS 8
Functionals and their Variations 9
A Necessary Condition: The Euler Equation 11
Generalizations of Euler s Equation 16
231 Case of Several Variables 16
232 Case where / involves derivatives of
nth order 17
Particular Cases of the Euler Equation 19
241 Absence of x 19
242 Absence oft 21
243 Absence of x 22
244 f{x, x, t) is linear in x 24
Variational Problems with Constraints 26
251 Point and Differential Equation Constraints 26
252 Isoperimetric Constraint 28
Some Economic Applications 32
261 Dynamic Pure Competition 32
262 Dynamic Utility and Capital Accumulation 33
263 Capital Theory 34
264 Time Optimal Problem in Economic Planning 36
265 Optimal Education and Balanced Growth 37
266 Micro Foundations of Macro Models 40
267 Constrained Optimal Consumption Plan 41
268 Optimal Waste Disposal 42
269 The Perimetric Problem of Non-Renewable
Resources 44
Summary and Conclusion 45
XII
Page
Chapter 3 BOUNDARY CONDITIONS IN VARIATIONAL PROBLEMS 48
3 1 Two fixed End Point and Natural Boundary Problems 48
3 2 Variable End Points 50
3 3 Broken Extremals and the Erdman-Weierstrass
Corner Conditions 64
3 4 Canonical Form of the Euler Equation 72
3 5 Some Economic Applications 75
351 Dynamic Monopoly 75
352 Optimal Economic Growth 1~l
353 Capital Theory with Exhaustible Resources 81
354 Optimal Mining with Incomplete Exhaustion 85
3 6 Summary 88
Chapter 4 SECOND VARIATIONS AND SUFFICIENCY CONDITIONS 90
4 1 Introduction 90
4 2 Variations of Functionals 91
4 3 The Legendre Condition 92
4 4 The Jacobi Condition 93
4 5 The Weierstrass Condition for Strong Extrema 95
4 6 The Legendre-Clebsch Condition 98
4 7 Sufficient Conditions: An Important Special Case 102
4 8 Summary and Conclusion 105
Appendix to Chapter 4 109
Chapter 5 OPTIMAL CONTROL: THE VARIATIONAL APPROACH 110
5 1 Introduction 110
5 2 From the Calculus of Variations to Optimal
Control 110
5 3 Pontryagin s Maximum Principle 113
5 4 Transversality Conditions 122
541 Problems with Fixed Final Time T 123
542 Problems with Free Final Time T 124
543 Transversality Conditions in Infinite
Horizon Problems 130
5 5 Second Variations and Sufficient Conditions 135
5 6 Some Economic Applications 140
561 Dynamic Monopoly 140
562 Optimal Growth 141
563 Non-Renewable Resources 144
564 Optimal Population 146
565 Optimal Phasing of Deregulation 148
5 7 Summary and Conclusion 151
XIII
Page
Chapter 6 CONSTRAINED OPTIMAL CONTROL PROBLEMS 153
6 1 Introduction 153
6 2 Optimal Control with Equality Constraints 153
6 3 Optimal Control with Inequality Constraints 158
631 Bounded Control Variables 158
Application: Permanent Capital in the
Resource Industries 169
632 Bounded State Variables 171
Application: Optimal Investment in Physical
and Human Capital 176
6 4 Dynamic Programming, Hamilton-Jacobi Equation
and the Euler Equation 183
6 5 Summary and Conclusion 188
Appendix to Chapter 6 190
Chapter 7 LINEAR OPTIMAL CONTROL 193
7 1 Introduction 193
7 2 Bang Bang Control and Time Minimum Problem 195
Economic Application: Optimal Monetary Policy 202
7 3 Singular Control 205
7 4 Singular Control and the Calculus of Variations 213
7 5 Singularity and Controllability 214
7 6 Some Economic Applications 216
761 Optimal Economic Growth 216
762 Resource Economics 219
Reproducible Resources 220
Non-Renewable Resources 224
7 6 3 Optimal Domestic and Foreign Investment 226
7 7 Summary and Conclusion 233
Chapter 8 STABILIZATION CONTROL MODELS 234
8 1 Introduction 234
8 2 Linear Regulator Problems 235
8 3 Linear Tracking Problems 240
8 4 Controllability 245
8 5 Observability 247
8 6 Some Economic Applications 248
861 The Multiplier-Accelerator Model 248
862 Production and Inventory Stabilization Model 251
863 Economic Stabilization: The Austrian Case 253
8 7 Conclusion 255
XIV
Page
Chapter 9 DISCRETE CONTROL SYSTEMS 256
9 1 Introduction 256
9 2- Discrete Calculus of Variations 256
Example 9 1 Discrete Optimal Growth Model 258
9 3 Discrete Maximum Principle 261
Example 9 2 Optimal Management of Renewable
Resources 264
Example 9 3 Discrete Linear Regulator 266
Example 9 4 Linear Tracking and Economic
Stabilization 268
Example 9 5 Optimal Wage Price Control 273
Chapter 10 SENSITIVITY ANALYSIS 277
10 1 Introduction 277
10 2 Sensitivity Theory 278
10 3 Cross Sensitivity 281
10 4 Objective Functional Sensitivity 282
10 5 Stability and Sensitivity 283
10 6 Some Economic Applications 285
10 6 1 Tax and Taste Sensitivity and Cross
Sensitivity 285
10 6 2 Optimal Growth Model: Sensitivity and
Comparative Dynamics 287
10 7 Conclusion 291
Chapter 11 DIFFERENTIAL GAMES 293
11 1 Introduction 293
11 2 Game Theory 294
11 2 1 Two-Person Zero-Sum Games 295
11 2 2 Non-Zero Sum Games 304
11 2 3 Economic Applications 308
11 3 Differential Games 315
11 3 1 The Nash Equilibrium Solution 319
11 3 2 The Stackelberg Equilibrium Solution 321
11 3 3 Linear Quadratic Differential Games 324
11 3 4 Dynamic Programming and Differential Games 329
11 3 5 Some Tractable Differential Game Problems 330
11 3 6 Some Economic Applications 331
1 Dynamic Duopoly 331
2 Collective Bargaining 333
3 Arms Race Differential Games 336
4 Economic Growth and Distribution: A Class
Struggle Game 339
5 Economic Stabilization Game 342
11 4 Conclusion 344
Chapter 12 STABILITY OF OPTIMAL CONTROL 345
12 1 Introduction 345
12 2 Asymptotic Stability of Hamiltonian Systems 347
12 3 Asymptotic Stability of Hamiltonian Economic
Systems 353
XV
Page
12 3 1 Stability of Optimal Economic Growth
Models 354
12 3 2 Stability of Linear Regulator Model6 357
12 3 3 Summary and Some New Results 359
12 4 Stability, Correspondence Principle and Comparative
Statics 361
12 4 1 Comparative Statics and Optimal Growth
Models 363
12 4 2 Comparative Statics and Capital Theory 364
12 5 Structural Stability of Optimal Control 365
12 5 1 Structural Stability Concepts 366
12 5 2 Structural Stability of Hamiltonian Economic
Systems 367
12 5 3 Gyroscopic Forces in Hamiltonian Economic
Systems 369
12 6 Conclusion 372
Chapter 13 SOME ECONOMIC AND MANAGEMENT APPLICATIONS 373
13 1 Introduction 373
13 2 Some Economic Applications 374
13 2 1 Optimal Economic Growth 374
13 211 The One-Sector Optimal Growth Model 375
13212 Technical Progress in the Aggregate
Model 381
13 213 Two-Sector Models 381
13 214 The Multisectoral Optimal Growth Models 388
13 215 Numerical Methods for Optimal Growth
Models 390
13 2 2 Economic Stabilization Models 392
13 2 3 Dynamic Theory of the Firms 392
13 2 4 International Trade 393
13 2 5 Regional Economics 396
13 2 6 Optimal Urban Economics 399
13 2 7 Education, Labour Training and Human Capital 402
13 2 8 Natural Resources 403
13 2 9 Optimal Control of Pollution 403
13 2 10 Optimal Population Control 405
13 2 11 Optimal Control of the Armament Build-up 405
13 3 Some Management Science Applications: A Dynamic
Theory of the Managerial Firm 411
13 3 1 Optimal Financing Model 411
13 3 2 Optimal Production and Inventory Models 414
13 3 3 Marketing Models 414
13 3 4 Maintenance Models 418
13 4 Conclusion 420
MATHEMATICAL APPENDIX: REVIEW OF DIFFERENTIAL AND DIFFERENCE EQUATIONS
A I Introduction 421
A 2 Differential Equations 421
A21 First Order Linear Differential Equation Systems 423
A22 Fundamental Matrix 425
A23 The nth Order Linear Differential Equation 427
A24 Non-Homogeneous First Order Differential Equation
Systems • 427
XVI
Page
A 3 Difference Equations 431
A 4 Stability of Differential and Difference Equations 435
A 5 Phase Diagrams and Non-Linear Differential Equations 437
A 6 Isoclines 441
A 7 Non-Linear Differential Equations 444
A 8 Phase Diagrams of Difference Equations 447
A 9 Liapunov s Second (or Direct) Method 449
REFERENCES 453
INDEX 472
|
| any_adam_object | 1 |
| author | Tu, Pierre N. V. |
| author_facet | Tu, Pierre N. V. |
| author_role | aut |
| author_sort | Tu, Pierre N. V. |
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| building | Verbundindex |
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| discipline | Mathematik Wirtschaftswissenschaften Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| edition | 2., revised and enl. ed. |
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| indexdate | 2024-07-09T16:14:05Z |
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| language | English |
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| spelling | Tu, Pierre N. V. Verfasser aut Introductory optimization dynamics optimal control with economics and management applications Pierre N. V. Tu 2., revised and enl. ed. Berlin u.a. Springer 1991 XVI, 474 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Calcul des variations Commande, Théorie de la Optimisation mathématique Control theory Mathematical optimization Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Unternehmensleitung (DE-588)4233771-9 gnd rswk-swf Wirtschaftstheorie (DE-588)4079351-5 gnd rswk-swf Management (DE-588)4037278-9 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 s Management (DE-588)4037278-9 s DE-604 Wirtschaftstheorie (DE-588)4079351-5 s Kontrolltheorie (DE-588)4032317-1 s DE-188 Unternehmensleitung (DE-588)4233771-9 s 1\p DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002796067&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Tu, Pierre N. V. Introductory optimization dynamics optimal control with economics and management applications Calcul des variations Commande, Théorie de la Optimisation mathématique Control theory Mathematical optimization Kontrolltheorie (DE-588)4032317-1 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Unternehmensleitung (DE-588)4233771-9 gnd Wirtschaftstheorie (DE-588)4079351-5 gnd Management (DE-588)4037278-9 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4121428-6 (DE-588)4233771-9 (DE-588)4079351-5 (DE-588)4037278-9 |
| title | Introductory optimization dynamics optimal control with economics and management applications |
| title_auth | Introductory optimization dynamics optimal control with economics and management applications |
| title_exact_search | Introductory optimization dynamics optimal control with economics and management applications |
| title_full | Introductory optimization dynamics optimal control with economics and management applications Pierre N. V. Tu |
| title_fullStr | Introductory optimization dynamics optimal control with economics and management applications Pierre N. V. Tu |
| title_full_unstemmed | Introductory optimization dynamics optimal control with economics and management applications Pierre N. V. Tu |
| title_short | Introductory optimization dynamics |
| title_sort | introductory optimization dynamics optimal control with economics and management applications |
| title_sub | optimal control with economics and management applications |
| topic | Calcul des variations Commande, Théorie de la Optimisation mathématique Control theory Mathematical optimization Kontrolltheorie (DE-588)4032317-1 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Unternehmensleitung (DE-588)4233771-9 gnd Wirtschaftstheorie (DE-588)4079351-5 gnd Management (DE-588)4037278-9 gnd |
| topic_facet | Calcul des variations Commande, Théorie de la Optimisation mathématique Control theory Mathematical optimization Kontrolltheorie Optimale Kontrolle Unternehmensleitung Wirtschaftstheorie Management |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002796067&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT tupierrenv introductoryoptimizationdynamicsoptimalcontrolwitheconomicsandmanagementapplications |