Dynamic optimization: the calculus of variations and optimal control in economics and management
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
North Holland
1981
|
| Ausgabe: | 2. print. |
| Schriftenreihe: | Dynamic economics
4 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 331 S. |
| ISBN: | 0444004246 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804136098897592320 |
|---|---|
| adam_text | Contents
Preface ix
PARTI. CALCULUS OF VARIATIONS 1
Section 1. Introduction 3
production, growth, investment
Section 2. Example Solved 11
Section 3. Simplest Problem—Euler Equation 14
Section 4. Examples and Interpretations 20
production, consumption
Section 5. Solving the Euler Equation in Special Cases 28
production, investment, pricing, exhaustible resource
Section 6. Second Order Conditions 37
Section 7. Isoperimetric Problem 43
exhaustible resource
Section 8. Free End Value 48
checking systems that may fail
Section 9. Free Horizon—Transversality Conditions 53
production, consumption, exhaustible resource
Section 10. Equality Constrained Endpoint 61
minority neighborhood
vi Contents
Section 11. Salvage Value 66
research and development
Section 12. Inequality Constrained Endpoint 72
land use
Section 13. Comers 79
Section 14. Inequality Constraints in (t, x) 83
production
Section 15. Infinite Horizon Autonomous Problems 88
Section 16. Most Rapid Approach Paths 90
advertising, investment, fishing
Section 17. Diagrammatic Analysis 95
growth
Section 18. Several Functions 104
PART II. OPTIMAL CONTROL 109
Section 1. Introduction HI
production planning, growth, investment
Section 2. Simplest Problem—Necessary Conditions 114
new product pricing
Section 3. Sufficiency 122
Section 4. Interpretations 125
investment
Section 5. Several Variables 130
Section 6. Fixed Endpoint Problems 135
production, growth with an exhaustible resource
Section 7. Various Endpoint Conditions 143
consumption
Section 8. Discounting, Current Values, Comparative Dynamics 151
investment, pollution
Section 9. Equilibria in Infinite Horizon Autonomous Problems 159
advertising, growth, fishing
Contents vii
Section 10. Bounded Controls 170
production, machine maintenance and sale, human capital
Section 11. Further Control Constraint 180
Section 12. Discontinuous and Bang Bang Control 186
investment, machine maintenance
Section 13. Singular Solutions and Most Rapid Approach Paths 193
road building, investment, advertising, growth
Section 14. The Pontryagin Maximum Principle, Existence 201
Section 15. Further Sufficiency Theorems 204
growth, limit pricing
Section 16. Alternative Formulations 212
Section 17. State Variable Inequality Constraints 215
pollution, dividends
Section 18. Jumps in the State Variable 226
product diversity
Section 19. Delayed Response 233
limit pricing, investment
Section 20. Dynamic Programming 238
Section 21. Stochastic Optimal Control 243
consumption and investment in risky and riskless assets
APPENDIX A. CALCULUS AND NONLINEAR
PROGRAMMING 251
Section 1. Calculus Techniques 253
Section 2. Mean Value Theorems 256
Section 3. Concave and Convex Functions 260
Section 4. Maxima and Minima 265
Section 5. Equality Constrained Optimization 269
Section 6. Inequality Constrained Optimization 275
Section 7. Line Integrals and Green s Theorem 282
vifi Contents
APPENDIX B. DIFFERENTIAL EQUATIONS 285
Section 1. Introduction 287
Section 2. Linear First Order Differential Equations 290
Section 3. Linear Second Order Differential Equations 294
Section 4. Linear nth Order Differential Equations 301
Section 5. A Pair of Linear Equations 306
Section 6. Existence and Uniqueness of Solutions 312
References 315
Author Index 325
Subject Index 329
|
| adam_txt |
Contents
Preface ix
PARTI. CALCULUS OF VARIATIONS 1
Section 1. Introduction 3
production, growth, investment
Section 2. Example Solved 11
Section 3. Simplest Problem—Euler Equation 14
Section 4. Examples and Interpretations 20
production, consumption
Section 5. Solving the Euler Equation in Special Cases 28
production, investment, pricing, exhaustible resource
Section 6. Second Order Conditions 37
Section 7. Isoperimetric Problem 43
exhaustible resource
Section 8. Free End Value 48
checking systems that may fail
Section 9. Free Horizon—Transversality Conditions 53
production, consumption, exhaustible resource
Section 10. Equality Constrained Endpoint 61
minority neighborhood
vi Contents
Section 11. Salvage Value 66
research and development
Section 12. Inequality Constrained Endpoint 72
land use
Section 13. Comers 79
Section 14. Inequality Constraints in (t, x) 83
production
Section 15. Infinite Horizon Autonomous Problems 88
Section 16. Most Rapid Approach Paths 90
advertising, investment, fishing
Section 17. Diagrammatic Analysis 95
growth
Section 18. Several Functions 104
PART II. OPTIMAL CONTROL 109
Section 1. Introduction HI
production planning, growth, investment
Section 2. Simplest Problem—Necessary Conditions 114
new product pricing
Section 3. Sufficiency 122
Section 4. Interpretations 125
investment
Section 5. Several Variables 130
Section 6. Fixed Endpoint Problems 135
production, growth with an exhaustible resource
Section 7. Various Endpoint Conditions 143
consumption
Section 8. Discounting, Current Values, Comparative Dynamics 151
investment, pollution
Section 9. Equilibria in Infinite Horizon Autonomous Problems 159
advertising, growth, fishing
Contents vii
Section 10. Bounded Controls 170
production, machine maintenance and sale, human capital
Section 11. Further Control Constraint 180
Section 12. Discontinuous and Bang Bang Control 186
investment, machine maintenance
Section 13. Singular Solutions and Most Rapid Approach Paths 193
road building, investment, advertising, growth
Section 14. The Pontryagin Maximum Principle, Existence 201
Section 15. Further Sufficiency Theorems 204
growth, limit pricing
Section 16. Alternative Formulations 212
Section 17. State Variable Inequality Constraints 215
pollution, dividends
Section 18. Jumps in the State Variable 226
product diversity
Section 19. Delayed Response 233
limit pricing, investment
Section 20. Dynamic Programming 238
Section 21. Stochastic Optimal Control 243
consumption and investment in risky and riskless assets
APPENDIX A. CALCULUS AND NONLINEAR
PROGRAMMING 251
Section 1. Calculus Techniques 253
Section 2. Mean Value Theorems 256
Section 3. Concave and Convex Functions 260
Section 4. Maxima and Minima 265
Section 5. Equality Constrained Optimization 269
Section 6. Inequality Constrained Optimization 275
Section 7. Line Integrals and Green's Theorem 282
vifi Contents
APPENDIX B. DIFFERENTIAL EQUATIONS 285
Section 1. Introduction 287
Section 2. Linear First Order Differential Equations 290
Section 3. Linear Second Order Differential Equations 294
Section 4. Linear nth Order Differential Equations 301
Section 5. A Pair of Linear Equations 306
Section 6. Existence and Uniqueness of Solutions 312
References 315
Author Index 325
Subject Index 329 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Kamien, Morton I. Schwartz, Nancy L. |
| author_facet | Kamien, Morton I. Schwartz, Nancy L. |
| author_role | aut aut |
| author_sort | Kamien, Morton I. |
| author_variant | m i k mi mik n l s nl nls |
| building | Verbundindex |
| bvnumber | BV022126707 |
| classification_rvk | SK 880 |
| ctrlnum | (OCoLC)248125728 (DE-599)BVBBV022126707 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.622 |
| dewey-search | 519.622 |
| dewey-sort | 3519.622 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. print. |
| format | Book |
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| genre | Aufsatzsammlung - Dynamische Optimierung Aufsatzsammlung - Infinitesimalrechnung |
| genre_facet | Aufsatzsammlung - Dynamische Optimierung Aufsatzsammlung - Infinitesimalrechnung |
| id | DE-604.BV022126707 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:16:30Z |
| indexdate | 2024-07-09T20:51:00Z |
| institution | BVB |
| isbn | 0444004246 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015341355 |
| oclc_num | 248125728 |
| open_access_boolean | |
| owner | DE-706 |
| owner_facet | DE-706 |
| physical | 331 S. |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | North Holland |
| record_format | marc |
| series | Dynamic economics |
| series2 | Dynamic economics |
| spelling | Kamien, Morton I. Verfasser aut Dynamic optimization the calculus of variations and optimal control in economics and management 2. print. New York [u.a.] North Holland 1981 331 S. txt rdacontent n rdamedia nc rdacarrier Dynamic economics 4 Mathematik (DE-588)4037944-9 gnd rswk-swf Wirtschaftswissenschaften (DE-588)4066528-8 gnd rswk-swf Management (DE-588)4037278-9 gnd rswk-swf Dynamische Optimierung (DE-588)4125677-3 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Aufsatzsammlung - Dynamische Optimierung Aufsatzsammlung - Infinitesimalrechnung Mathematik (DE-588)4037944-9 s DE-604 Optimale Kontrolle (DE-588)4121428-6 s Dynamische Optimierung (DE-588)4125677-3 s Optimierung (DE-588)4043664-0 s Kontrolltheorie (DE-588)4032317-1 s Variationsrechnung (DE-588)4062355-5 s 1\p DE-604 Management (DE-588)4037278-9 s 2\p DE-604 Wirtschaftswissenschaften (DE-588)4066528-8 s 3\p DE-604 4\p DE-604 Schwartz, Nancy L. Verfasser aut Dynamic economics 4 (DE-604)BV001892227 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015341355&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kamien, Morton I. Schwartz, Nancy L. Dynamic optimization the calculus of variations and optimal control in economics and management Dynamic economics Mathematik (DE-588)4037944-9 gnd Wirtschaftswissenschaften (DE-588)4066528-8 gnd Management (DE-588)4037278-9 gnd Dynamische Optimierung (DE-588)4125677-3 gnd Variationsrechnung (DE-588)4062355-5 gnd Optimierung (DE-588)4043664-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4066528-8 (DE-588)4037278-9 (DE-588)4125677-3 (DE-588)4062355-5 (DE-588)4043664-0 (DE-588)4121428-6 (DE-588)4032317-1 |
| title | Dynamic optimization the calculus of variations and optimal control in economics and management |
| title_auth | Dynamic optimization the calculus of variations and optimal control in economics and management |
| title_exact_search | Dynamic optimization the calculus of variations and optimal control in economics and management |
| title_exact_search_txtP | Dynamic optimization the calculus of variations and optimal control in economics and management |
| title_full | Dynamic optimization the calculus of variations and optimal control in economics and management |
| title_fullStr | Dynamic optimization the calculus of variations and optimal control in economics and management |
| title_full_unstemmed | Dynamic optimization the calculus of variations and optimal control in economics and management |
| title_short | Dynamic optimization |
| title_sort | dynamic optimization the calculus of variations and optimal control in economics and management |
| title_sub | the calculus of variations and optimal control in economics and management |
| topic | Mathematik (DE-588)4037944-9 gnd Wirtschaftswissenschaften (DE-588)4066528-8 gnd Management (DE-588)4037278-9 gnd Dynamische Optimierung (DE-588)4125677-3 gnd Variationsrechnung (DE-588)4062355-5 gnd Optimierung (DE-588)4043664-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| topic_facet | Mathematik Wirtschaftswissenschaften Management Dynamische Optimierung Variationsrechnung Optimierung Optimale Kontrolle Kontrolltheorie Aufsatzsammlung - Dynamische Optimierung Aufsatzsammlung - Infinitesimalrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015341355&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001892227 |
| work_keys_str_mv | AT kamienmortoni dynamicoptimizationthecalculusofvariationsandoptimalcontrolineconomicsandmanagement AT schwartznancyl dynamicoptimizationthecalculusofvariationsandoptimalcontrolineconomicsandmanagement |