Optimal control theory: applications to management science and economics
This new 4th edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It introduces students to the concept of the maximum principle in continuous (as well as discrete) time by combining dynamic programming and Kuhn-Tucker theory. Whi...
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| Ausgabe: | Fourth edition |
| Schriftenreihe: | Springer Texts in Business and Economics
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| Zusammenfassung: | This new 4th edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It introduces students to the concept of the maximum principle in continuous (as well as discrete) time by combining dynamic programming and Kuhn-Tucker theory. While some mathematical background is needed, the emphasis of the book is not on mathematical rigor, but on modeling realistic situations encountered in business and economics. It applies optimal control theory to the functional areas of management including finance, production and marketing, as well as the economics of growth and of natural resources. In addition, it features material on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework. Exercises are included in each chapter, while the answers to selected exercises help deepen readers’ understanding of the material covered. Also included are appendices of supplementary material on the solution of differential equations, the calculus of variations and its ties to the maximum principle, and special topics including the Kalman filter, certainty equivalence, singular control, a global saddle point theorem, Sethi-Skiba points, and distributed parameter systems.Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as the foundation for the book, in which the author applies it to business management problems developed from his own research and classroom instruction. The new edition has been refined and updated, making it a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers interested in applying dynamic optimization in their fields |
| Beschreibung: | xxvii, 506 Seiten Illustrationen, Diagramme 961 grams |
| ISBN: | 9783030917449 |
Internformat
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| 250 | |a Fourth edition | ||
| 264 | 1 | |a Cham |b Springer |c 2021 | |
| 300 | |a xxvii, 506 Seiten |b Illustrationen, Diagramme |c 961 grams | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer Texts in Business and Economics | |
| 520 | |a This new 4th edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It introduces students to the concept of the maximum principle in continuous (as well as discrete) time by combining dynamic programming and Kuhn-Tucker theory. While some mathematical background is needed, the emphasis of the book is not on mathematical rigor, but on modeling realistic situations encountered in business and economics. It applies optimal control theory to the functional areas of management including finance, production and marketing, as well as the economics of growth and of natural resources. In addition, it features material on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework. Exercises are included in each chapter, while the answers to selected exercises help deepen readers’ understanding of the material covered. Also included are appendices of supplementary material on the solution of differential equations, the calculus of variations and its ties to the maximum principle, and special topics including the Kalman filter, certainty equivalence, singular control, a global saddle point theorem, Sethi-Skiba points, and distributed parameter systems.Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as the foundation for the book, in which the author applies it to business management problems developed from his own research and classroom instruction. The new edition has been refined and updated, making it a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers interested in applying dynamic optimization in their fields | ||
| 650 | 4 | |a bicssc | |
| 650 | 4 | |a bisacsh | |
| 650 | 4 | |a Operations research | |
| 650 | 4 | |a Management science | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Calculus of variations | |
| 650 | 4 | |a Econometrics | |
| 650 | 4 | |a Industrial engineering | |
| 650 | 4 | |a Production engineering | |
| 650 | 4 | |a System theory | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Operations research | |
| 650 | 0 | 7 | |a Kontrolltheorie |0 (DE-588)4032317-1 |2 gnd |9 rswk-swf |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-033599051 | |
Datensatz im Suchindex
| _version_ | 1813260576389857280 |
|---|---|
| adam_text |
CONTENTS
1
WHAT
IS OPTIMAL CONTROL
THEORY? 1
1.1
BASIC
CONCEPTS AND DEFINITIONS
2
1.2
FORMULATION
OF SIMPLE CONTROL MODELS
3
1.3
HISTORY
OF OPTIMAL CONTROL THEORY
7
1.4
NOTATION
AND CONCEPTS
USED 9
1.4.1
DIFFERENTIATING
VECTORS AND MATRICES WITH
RESPECT
TO SCALARS 10
1.4.2
DIFFERENTIATING
SCALARS WITH RESPECT TO VECTORS 10
1.4.3
DIFFERENTIATING
VECTORS WITH RESPECT TO VECTORS 11
1.4.4
PRODUCT
RULE FOR DIFFERENTIATION 13
1.4.5
MISCELLANY
13
1.4.6
CONVEX
SET AND CONVEX HULL
16
1.4.7
CONCAVE
AND CONVEX FUNCTIONS 17
1.4.8
AFFINE
FUNCTION AND HOMOGENEOUS FUNCTION
OF DEGREE K
18
1.4.9
SADDLE
POINT
18
1.4.10
LINEAR INDEPENDENCE AND RANK OF A MATRIX
19
1.5
PLAN
OF THE BOOK 19
EXERCISES
FOR CHAP. 1
20
REFERENCES
22
2
THE
MAXIMUM PRINCIPLE: CONTINUOUS TIME
25
2.1
STATEMENT
OF THE PROBLEM 25
2.1.1
THE
MATHEMATICAL MODEL
25
2.1.2
CONSTRAINTS
26
2.1.3
THE
OBJECTIVE
FUNCTION
26
2.1.4
THE
OPTIMAL CONTROL PROBLEM 27
2.2
DYNAMIC
PROGRAMMING AND THE MAXIMUM PRINCIPLE 30
2.2.1
THE
HAMILTON-JACOBI-BELLMAN
EQUATION 30
2.2.2
DERIVATION
OF THE ADJOINT EQUATION 33
2.2.3
THE
MAXIMUM PRINCIPLE 35
2.2.4
ECONOMIC
INTERPRETATIONS OF THE MAXIMUM PRINCIPLE
37
2.3
SIMPLE
EXAMPLES 39
XVII
XVIII
CONTENTS
CONTENTS
2.4
SUFFICIENCY
CONDITIONS
2.5
SOLVING
A TPBVP
BY USING EXCEL
EXERCISES
FOR CHAP. 2
REFERENCES
48
6.1.5
OPTIMALITY
OF A
LINEAL
52
6.1.6
ANALYSIS
WITH A NONNI
55
CONSTRAINT
62
6.2 THE
WHEAT TRADING MODEL
3
THE
MAXIMUM
PRINCIPLE: MIXED
INEQUALITY CONSTRAINTS
65
3.1
A
MAXIMUM PRINCIPLE FOR PROBLEMS WITH MIXED INEQUALITY
CONSTRAINTS
66
3.2
SUFFICIENCY
CONDITIONS
74
3.3
CURRENT-VALUE
FORMULATION
75
3.4
TRANSVERSALITY
CONDITIONS: SPECIAL CASES
80
3.5
FREE
TERMINAL TIME PROBLEMS
87
3.6
INFINITE
HORIZON AND STATIONARITY
96
3.7
MODEL
TYPES
101
EXERCISES
FOR CHAP. 3
105
REFERENCES
114
4
THE
MAXIMUM PRINCIPLE: PURE STATE
AND MIXED INEQUALITY
CONSTRAINTS
115
4.1
JUMPS
IN MARGINAL
VALUATIONS
116
4.2
THE
OPTIMAL CONTROL PROBLEM WITH
PURE AND MIXED
CONSTRAINTS
119
4.3
THE
MAXIMUM PRINCIPLE: DIRECT METHOD
121
4.4
SUFFICIENCY
CONDITIONS: DIRECT METHOD
124
4.5
THE
MAXIMUM PRINCIPLE: INDIRECT METHOD
125
4.6
CURRENT-VALUE
MAXIMUM PRINCIPLE:
INDIRECT METHOD
133
EXERCISES
FOR CHAP. 4
135
REFERENCES
144
5
APPLICATIONS TO FINANCE
145
5.1
THE
SIMPLE CASH
BALANCE PROBLEM
145
5.1.1
THE
MODEL
146
5.1.2
SOLUTION
BY THE MAXIMUM PRINCIPLE
147
5.2
OPTIMAL
FINANCING MODEL
150
5.2.1
THE
MODEL
151
5.2.2
APPLICATION
OF THE MAXIMUM
PRINCIPLE
152
5.2.3
SYNTHESIS
OF OPTIMAL CONTROL PATHS
156
5.2.4
SOLUTION
FOR THE INFINITE HORIZON PROBLEM
166
EXERCISES
FOR CHAP. 5
170
REFERENCES
173
6
APPLICATIONS TO
PRODUCTION AND INVENTORY
175
6.1
PRODUCTION-INVENTORY
SYSTEMS
176
6.1.1
THE
PRODUCTION-INVENTORY MODEL
176
6.1.2
SOLUTION
BY THE MAXIMUM PRINCIPLE
177
6.1.3
THE
INFINITE HORIZON SOLUTION
180
6.1.4
SPECIAL
CASES OF
TIME VARYING DEMANDS
181
6.2.1
THE
MODEL
6.2.2
SOLUTION
BY THE MAXIN
6.2.3
SOLUTION
OF A SPECIAL
6.2.4
THE
WHEAT TRADING M
6.3
DECISION
HORIZONS
AND FORECA5
6.3.1
HORIZONS
FOR THE
WHE,
SHORT-SELLING
6.3.2
HORIZONS
FOR
THE WHE,
SHORT-SELLING
AND A W
EXERCISES
FOR
CHAP. 6
REFERENCES
7
APPLICATIONS
TO MARKETING
7.1
THE
NERLOVE-ARROW
ADVERTISIN
7.1.1
THE
MODEL
7.1.2
SOLUTION
BY
THE MAXIN
7.1.3
CONVEX
ADVERTISING C
7.2
THE
VIDALE-WOLFE
ADVERTISING
7.2.1
OPTIMAL
CONTROL
FORM
VIDALE-WOLFE
MODEL.
7.2.2
SOLUTION
USING
GREEN'
7.2.3
SOLUTION
WHEN
Q IS S
7.2.4
SOLUTION
WHEN T IS IN
EXERCISES FOR THIS
CHAP. 7
REFERENCES
8
THE
MAXIMUM
PRINCIPLE: DISCRETE 1
8.1
NONLINEAR
PROGRAMMING PROBLT
8.1.1
LAGRANGE
MULTIPLIERS .
8.1.2
EQUALITY
AND
INEQUALIT
8.1.3
CONSTRAINT
QUALIFICATIC
8.1.4
THEOREMS
FROM NONLII
8.2
A
DISCRETE
MAXIMUM PRINCIPLE
8.2.1
A
DISCRETE-TIME
OPTII
8.2.2
A
DISCRETE
MAXIMUM
8.2.3
EXAMPLES
8.3
A
GENERAL DISCRETE MAXIMUM
EXERCISES FOR
CHAP. 8
REFERENCES
CONTENTS
XIX
6.1.5
OPTIMALITY
OF
A LINEAR DECISION RULE
184
6.1.6
ANALYSIS
WITH A
NONNEGATIVE PRODUCTION
CONSTRAINT
186
6.2
THE
WHEAT
TRADING MODEL
188
6.2.1
THE
MODEL
188
6.2.2
SOLUTION
BY
THE MAXIMUM PRINCIPLE
189
6.2.3
SOLUTION
OF A
SPECIAL CASE
190
6.2.4
THE
WHEAT TRADING MODEL WITH NO SHORT-SELLING
193
6.3
DECISION
HORIZONS AND FORECAST
HORIZONS
195
6.3.1
HORIZONS
FOR THE WHEAT TRADING
MODEL WITH NO
SHORT-SELLING
197
6.3.2
HORIZONS
FOR THE WHEAT
TRADING MODEL WITH
NO
SHORT-SELLING
AND A WAREHOUSING CONSTRAINT
198
EXERCISES FOR CHAP. 6
203
REFERENCES
205
7
APPLICATIONS
TO
MARKETING
207
7.1
THE
NERLOVE-ARROW ADVERTISING
MODEL
208
7.1.1
THE
MODEL
208
7.1.2
SOLUTION
BY THE MAXIMUM
PRINCIPLE
210
7.1.3
CONVEX
ADVERTISING COST AND RELAXED
CONTROLS 213
7.2
THE
VIDALE-WOLFE ADVERTISING
MODEL
216
7.2.1
OPTIMAL
CONTROL FORMULATION
FOR THE
VIDALE-WOLFE MODEL
216
7.2.2
SOLUTION
USING GREEN'S THEOREM
WHEN Q IS LARGE
218
7.2.3
SOLUTION
WHEN Q IS SMALL
225
7.2.4
SOLUTION
WHEN T IS INFINITE
227
EXERCISES
FOR THIS
CHAP. 7
230
REFERENCES
237
8
THE
MAXIMUM
PRINCIPLE: DISCRETE TIME
239
8.1
NONLINEAR
PROGRAMMING PROBLEMS
239
8.1.1
LAGRANGE
MULTIPLIERS
240
8.1.2
EQUALITY
AND
INEQUALITY CONSTRAINTS
242
8.1.3
CONSTRAINT
QUALIFICATION
246
8.1.4
THEOREMS
FROM NONLINEAR PROGRAMMING
247
8.2
A
DISCRETE
MAXIMUM PRINCIPLE
248
8.2.1
A
DISCRETE-TIME OPTIMAL
CONTROL PROBLEM
248
8.2.2
A
DISCRETE MAXIMUM
PRINCIPLE
249
8.2.3
EXAMPLES
251
8.3
A
GENERAL DISCRETE
MAXIMUM PRINCIPLE
254
EXERCISES
FOR
CHAP. 8
256
REFERENCES
259
CONTENTS
CONTENTS
9
MAINTENANCE AND
REPLACEMENT
261
11.3
A
POLLUTION
CONTROL
MODEL
9.1
A
SIMPLE
MAINTENANCE AND REPLACEMENT
MODEL
261
1 1.3.1
MODEL
FORMULATION
9.1.1
THE
MODEL
262
11.3.2
SOLUTION
BY
THE
MAXIMU
9.1.2
SOLUTION
BY THE MAXIMUM PRINCIPLE
263
11.3.3
PHASE
DIAGRAM
ANALYSIS
9.1.3
A
NUMERICAL EXAMPLE
265
11.4
AN
ADVERSE
SELECTION
MODEL .
9.1.4
AN
EXTENSION
267
11.4.1
MODEL
FORMULATION
9.2
MAINTENANCE
AND
REPLACEMENT FOR A MACHINE SUBJECT
11.4.2
THE
IMPLEMENTATION
PRO
TO
FAILURE
268
11.4.3
THE
OPTIMIZATION
PROB!(
9.2.1
THE
MODEL
269
11.5
MISCELLANEOUS
APPLICATIONS
9.2.2
OPTIMAL POLICY
271
EXERCISES
FOR
CHAP. 11
9.2.3
DETERMINATION
OF THE SALE DATE 273
REFERENCES
9.3
CHAIN
OF MACHINES
274
9.3.1
THE
MODEL
274
12
STOCHASTIC
OPTIMAL
CONTROL
9.3.2
SOLUTION
BY THE DISCRETE MAXIMUM PRINCIPLE
276
12.1
STOCHASTIC
OPTIMAL
CONTROL
9.3.3
SPECIAL
CASE OF BANG-BANG
CONTROL
277
12.2
A
STOCHASTIC
PRODUCTION
INVENTOR
9.3.4
INCORPORATION
INTO THE
WAGNER-WHITIN FRAMEWORK
12.2.1
SOLUTION
FOR
THE PRODUCTI
FOR
A COMPLETE SOLUTION
278
12.3
THE
SETHI ADVERTISING MODEL .
9.3.5
A
NUMERICAL EXAMPLE
279
12.4 AN OPTIMAL CONSUMPTION-INVESTA
EXERCISES
FOR CHAP. 9
283
12.5
CONCLUDING
REMARKS
REFERENCES
286
EXERCISES FOR CHAP. 12
REFERENCES
10
APPLICATIONS TO NATURAL RESOURCES
10.1
THE SOLE-OWNER FISHERY RESOURCE MODEL
289
289
13
DIFFERENTIAL
GARNES
10.1.1
THE
DYNAMICS OF FISHERY MODELS
290
13.1
TWO-PERSON
ZERO-SUM
DIFFERENTI,
10.1.2
THE SOLE OWNER MODEL
291
13.2
NASH
DIFFERENTIAL
GAMES
10.1.3
SOLUTION BY GREEN'S THEOREM
291
13.2.1
OPEN-LOOP
NASH
SOLUTIC
10.2
AN OPTIMAL FOREST THINNING MODEL
295
13.2.2
FEEDBACK
NASH
SOLUTION
10.2.1
THE
FORESTRY MODEL
295
13.2.3
AN
APPLICATION
TO
COMR
10.2.2
DETERMINATION
OF OPTIMAL THINNING
296
RESOURCES
10.2.3
A
CHAIN OF FORESTS MODEL
298
13.3
A
FEEDBACK
NASH
STOCHASTIC
DIFF
10.3
AN EXHAUSTIBLE RESOURCE MODEL
301
13.4
A
FEEDBACK
STACKELBERG
STOCHAST
10.3.1
FORMULATION OF THE MODEL
302
OF
COOPERATIVE
ADVERTISING
10.3.2
SOLUTION BY THE MAXIMUM PRINCIPLE
304
EXERCISES
FOR
CHAP.
13
EXERCISES
FOR CHAP. 10
307
REFERENCES
REFERENCES
310
A
SOLUTIONS
OF
LINEAR
DIFFERENTIAL
EQUAT
11
APPLICATIONS TO ECONOMICS
313
A.1
FIRST-ORDER
LINEAR
EQUATIONS
11.1
MODELS
OF OPTIMAL ECONOMIC GROWTH
313
A.2
SECOND-ORDER
LINEAR
EQUATIONS
\A
11.1.1
AN
OPTIMAL CAPITAL ACCUMULATION MODEL
314
A.3
SYSTEM
OF
FIRST-ORDER
LINEAR EQU
11.1.2
SOLUTION BY THE MAXIMUM PRINCIPLE
314
A.4
SOLUTION OF
LINEAR
TWO-POINT
BOT
11.1.3
INTRODUCTION OF A GROWING LABOR FORCE
315
A.5
SOLUTIONS
OF
FINITE
DIFFERENCE
ECY
11.1.4
SOLUTION BY THE MAXIMUM PRINCIPLE
317
A.5.1
CHANGING
POLYNOMIALS
IT
11.2
A MODEL OF OPTIMAL EPIDEMIC CONTROL
320
FACTORIAL
POWERS
OF
K
11.2.1
FORMULATION OF THE MODEL
321
A.5.2
CHANGING
FACTORIAL
POWT
11.2.2
SOLUTION BY GREEN'S THEOREM
321
POWERS
OF
K
NTS
61
61
62
63
65
167
268
269
CONTENTS
XXI
11.3
A
POLLUTION CONTROL
MODEL
1
1.3.1
MODEL
FORMULATION
11.3.2
SOLUTION
BY THE MAXIMUM
PRINCIPLE
11.3.3
PHASE DIAGRAM ANALYSIS
11.4 AN ADVERSE
SELECTION MODEL
11.4.1
MODEL FORMULATION
11.4.2
THE IMPLEMENTATION
PROBLEM
11.4.3
THE
OPTIMIZATION
PROBLEM
11.5
MISCELLANEOUS APPLICATIONS
324
324
325
326
328
329
330
331
336
2
71
EXERCISES FOR CHAP. 11
337
273
REFERENCES
340
74
74
12
STOCHASTIC OPTIMAL
CONTROL
345
276
277
12.1
STOCHASTIC OPTIMAL CONTROL
12.2
A
STOCHASTIC PRODUCTION INVENTORY MODEL
346
349
12.2.1
SOLUTION FOR THE PRODUCTION
PLANNING PROBLEM
351
278
12.3
THE
SETHI
ADVERTISING MODEL
354
279
12.4
AN
OPTIMAL CONSUMPTION-INVESTMENT PROBLEM 357
283
12.5
CONCLUDING REMARKS
362
286
EXERCISES
FOR CHAP. 12
REFERENCES
362
364
289
289
290
291
13
DIFFERENTIAL
GARNES
13.1
TWO-PERSON
ZERO-SUM DIFFERENTIAL
GARNES
13.2
NASH
DIFFERENTIAL GARNES
367
367
369
291
13.2.1
OPEN-LOOP
NASH SOLUTION
369
295
13.2.2
FEEDBACK
NASH SOLUTION
370
295
13.2.3
AN
APPLICATION TO
COMMON-PROPERTY FISHERY
296
RESOURCES
371
298
301
13.3
A
FEEDBACK NASH STOCHASTIC
DIFFERENTIAL GARNE IN
ADVERTISING
13.4 A
FEEDBACK STACKELBERG
STOCHASTIC
DIFFERENTIAL GAME
373
302
OF
COOPERATIVE ADVERTISING
377
304
307
EXERCISES
FOR
CHAP. 13
REFERENCES
386
389
310
A
SOLUTIONS OF
LINEAR DIFFERENTIAL
EQUATIONS
391
313
A.1
FIRST-ORDER LINEAR
EQUATIONS
391
313
A.2
SECOND-ORDER
LINEAR
EQUATIONS WITH CONSTANT
COEFFICIENTS
392
314
A.3
SYSTEM OF FIRST-ORDER
LINEAR EQUATIONS
393
314
A.4
SOLUTION OF LINEAR
TWO-POINT BOUNDARY
VALUE PROBLEMS
394
315
A.5
SOLUTIONS
OF FINITE DIFFERENCE
EQUATIONS
395
317
A.5.1
CHANGING
POLYNOMIALS
IN POWERS OF K INTO
320
FACTORIAL
POWERS OF K
396
321
A.5.2
CHANGING
FACTORIAL POWERS
OF K INTO ORDINARY
321
POWERS OF
K
397
LIST
OF
FIGURES
FIG.
1.1
FIG. 1.2
FIG. 1.3
FIG. 1.4
FIG.
2.1
FIG. 2.2
FIG. 2.3
FIG. 2.4
FIG. 2.5
FIG. 2.6
FIG. 2.7
FIG. 2.8
FIG. 3.1
FIG.
3.2
FIG. 4.1
FIG.
4.2
FIG. 4.3
FIG.
4.4
FIG. 4.5
FIG. 5.1
FIG. 5.2
FIG.
5.3
FIG.
5.4
FIG. 5.5
FIG.
5.6
FIG.
5.7
FIG. 5.8
FIG. 6.1
FIG. 6.2
FIG.
6.3
FIG. 6.4
FIG.
6.5
THE
BRACHISTOCHRONE
PROBLEM
ILLUSTRATION
OF LEFT
AND RIGHT
LIN
A CONCAVE
FUNCTION
AN
ILLUSTRATION
OF A
SADDLE
POII
AN
OPTIMAL
PATH IN
THE
STATE-TII
OPTIMAL
STATE
AND
ADJOINT
TRAJE
OPTIMAL
STATE
AND ADJOINT
TRAJE
OPTIMAL
TRAJECTORIES
FOR
EXAMI
OPTIMAL
CONTROL
FOR
EXAMPLE 2
THE
FLOWCHART
FOR
EXAMPLE 2.8
SOLUTION
OF
TPBVP BY
EXCEL
.
WATER
RESERVOIR OF
EXERCISE
2.1
STATE
AND
ADJOINT
TRAJECTORIES IR.
MINIMUM
TIME
OPTIMAL
RESPON
FEASIBLE
STATE
SPACE AND
OPTIRR
EXAMPLES 4.1
AND 4.4
STATE
AND
ADJOINT
TRAJECTORIES
IN
ADJOINT
TRAJECTORY
FOR
EXAMPLE
TWO-RESERVOIR
SYSTEM OF
EXERC
FEASIBLE
SPACE
FOR EXERCISE
4.2
OPTIMAL
POLICY SHOWN
IN
(XI, A
OPTIMAL POLICY
SHOWN
IN
(T,
AE2
CASE A: G
YY R
CASE
B: G R
OPTIMAL
PATH
FOR CASE
A: G
YY R
OPTIMAL
PATH
FOR CASE B: G R
SOLUTION
FOR
EXERCISE
5.4
ADJOINT
TRAJECTORIES
FOR EXERCIS
SOLUTION
OF EXAMPLE
6.1
WITH 1
SOLUTION
OF EXAMPLE
6.1
WITH 1
SOLUTION
OF
EXAMPLE
6.1 WITH
1
OPTIMAL
PRODUCTION
RATE AND
IN
INITIAL
INVENTORIES
THE
PRICE
TRAJECTORY (6.56)
CONTENTS
B
CALCULUS
OF
VARIATIONS AND
OPTIMAL
CONTROL
THEORY
399
B.1
THE
SIMPLEST
VARIATIONAL
PROBLEM
399
B.2
THE
EULER-LAGRANGE
EQUATION
400
B.3
THE
SHORTEST
DISTANCE
BETWEEN
TWO POINTS
AN THE
PLANE
403
B.4
THE
BRACHISTOCHRONE
PROBLEM
404
B.5
THE
WEIERSTRASS-ERDMANN
CORNER
CONDITIONS
406
B.6
LEGENDRE'S
CONDITIONS:
THE
SECOND VARIATION
408
B.7
NECESSARY
CONDITION
FOR A
STRONG
MAXIMUM
409
B.8
RELATION
TO OPTIMAL
CONTROL
THEORY
410
C
AN
ALTERNATIVE
DERIVATION
OF THE
MAXIMUM
PRINCIPLE
413
C.1
NEEDLE-SHAPED
VARIATION
413
C.2
DERIVATION
OF THE
ADJOINT
EQUATION AND THE
MAXIMUM
PRINCIPLE
415
D
SPECIAL
TOPICS IN
OPTIMAL CONTROL
421
D.1
THE
KAIMAN
FILTER
421
D.2
WIENER
PROCESS
AND STOCHASTIC
CALCULUS
424
D.3
THE
KALMAN-BUCY
FILTER
426
D.4
LINEAR-QUADRATIC
PROBLEMS
427
D.4.1
CERTAINTY
EQUIVALENCE
OR
SEPARATION
PRINCIPLE
430
D.5
SECOND-ORDER
VARIATIONS
431
D.6
SINGULAR
CONTROL
434
D.7
GLOBAL
SADDLE
POINT THEOREM
435
D.8
THE
SETHI-SKIBA
POINTS
437
D.9
DISTRIBUTED
PARAMETER SYSTEMS
439
E
ANSWERS
TO SELECTED
EXERCISES
445
BIBLIOGRAPHY
451
INDEX
493 |
| adam_txt | |
| any_adam_object | 1 |
| any_adam_object_boolean | |
| author | Sethi, Suresh P. 1945- |
| author_GND | (DE-588)123987202 |
| author_facet | Sethi, Suresh P. 1945- |
| author_role | aut |
| author_sort | Sethi, Suresh P. 1945- |
| author_variant | s p s sp sps |
| building | Verbundindex |
| bvnumber | BV048218276 |
| classification_rvk | QH 721 SK 880 |
| ctrlnum | (OCoLC)1334025085 (DE-599)BVBBV048218276 |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | Fourth edition |
| format | Book |
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| id | DE-604.BV048218276 |
| illustrated | Illustrated |
| index_date | 2024-07-03T19:50:02Z |
| indexdate | 2024-10-18T14:00:40Z |
| institution | BVB |
| isbn | 9783030917449 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033599051 |
| oclc_num | 1334025085 |
| open_access_boolean | |
| owner | DE-29T DE-1050 DE-523 |
| owner_facet | DE-29T DE-1050 DE-523 |
| physical | xxvii, 506 Seiten Illustrationen, Diagramme 961 grams |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer Texts in Business and Economics |
| spelling | Sethi, Suresh P. 1945- Verfasser (DE-588)123987202 aut Optimal control theory applications to management science and economics Suresh P. Sethi Fourth edition Cham Springer 2021 xxvii, 506 Seiten Illustrationen, Diagramme 961 grams txt rdacontent n rdamedia nc rdacarrier Springer Texts in Business and Economics This new 4th edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It introduces students to the concept of the maximum principle in continuous (as well as discrete) time by combining dynamic programming and Kuhn-Tucker theory. While some mathematical background is needed, the emphasis of the book is not on mathematical rigor, but on modeling realistic situations encountered in business and economics. It applies optimal control theory to the functional areas of management including finance, production and marketing, as well as the economics of growth and of natural resources. In addition, it features material on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework. Exercises are included in each chapter, while the answers to selected exercises help deepen readers’ understanding of the material covered. Also included are appendices of supplementary material on the solution of differential equations, the calculus of variations and its ties to the maximum principle, and special topics including the Kalman filter, certainty equivalence, singular control, a global saddle point theorem, Sethi-Skiba points, and distributed parameter systems.Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as the foundation for the book, in which the author applies it to business management problems developed from his own research and classroom instruction. The new edition has been refined and updated, making it a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers interested in applying dynamic optimization in their fields bicssc bisacsh Operations research Management science Mathematical optimization Calculus of variations Econometrics Industrial engineering Production engineering System theory Control theory Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Unternehmensleitung (DE-588)4233771-9 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Stochastische optimale Kontrolle (DE-588)4207850-7 gnd rswk-swf Operations Research (DE-588)4043586-6 gnd rswk-swf Hardcover, Softcover / Wirtschaft/Allgemeines, Lexika Kontrolltheorie (DE-588)4032317-1 s Operations Research (DE-588)4043586-6 s DE-604 Mathematisches Modell (DE-588)4114528-8 s Stochastische optimale Kontrolle (DE-588)4207850-7 s Unternehmensleitung (DE-588)4233771-9 s Erscheint auch als Online-Ausgabe 978-3-030-91745-6 Vorangegangen ist 3. Auflage 978-3-319-98236-6 Digitalisierung Bibliothek HTW Berlin application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033599051&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sethi, Suresh P. 1945- Optimal control theory applications to management science and economics bicssc bisacsh Operations research Management science Mathematical optimization Calculus of variations Econometrics Industrial engineering Production engineering System theory Control theory Kontrolltheorie (DE-588)4032317-1 gnd Unternehmensleitung (DE-588)4233771-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Stochastische optimale Kontrolle (DE-588)4207850-7 gnd Operations Research (DE-588)4043586-6 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4233771-9 (DE-588)4114528-8 (DE-588)4207850-7 (DE-588)4043586-6 |
| title | Optimal control theory applications to management science and economics |
| title_auth | Optimal control theory applications to management science and economics |
| title_exact_search | Optimal control theory applications to management science and economics |
| title_exact_search_txtP | Optimal control theory applications to management science and economics |
| title_full | Optimal control theory applications to management science and economics Suresh P. Sethi |
| title_fullStr | Optimal control theory applications to management science and economics Suresh P. Sethi |
| title_full_unstemmed | Optimal control theory applications to management science and economics Suresh P. Sethi |
| title_short | Optimal control theory |
| title_sort | optimal control theory applications to management science and economics |
| title_sub | applications to management science and economics |
| topic | bicssc bisacsh Operations research Management science Mathematical optimization Calculus of variations Econometrics Industrial engineering Production engineering System theory Control theory Kontrolltheorie (DE-588)4032317-1 gnd Unternehmensleitung (DE-588)4233771-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Stochastische optimale Kontrolle (DE-588)4207850-7 gnd Operations Research (DE-588)4043586-6 gnd |
| topic_facet | bicssc bisacsh Operations research Management science Mathematical optimization Calculus of variations Econometrics Industrial engineering Production engineering System theory Control theory Kontrolltheorie Unternehmensleitung Mathematisches Modell Stochastische optimale Kontrolle Operations Research |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033599051&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sethisureshp optimalcontroltheoryapplicationstomanagementscienceandeconomics |