The long awaited second edition of Dynamic Optimization is now available. Clear exposition and numerous worked examples made the first edition the premier text on this subject. Now, the new edition is expanded and updated to include essential coverage of current developments on differential games, especially as they apply to important economic questions; new developments in comparative dynamics; and new material on optimal control with integral state equations.
The second edition of Dynamic Optimization provides expert coverage on:- methods of calculus of variations - optimal control - continuous dynamic programming - stochastic optimal control -differential games. The authors also include appendices on static optimization and on differential games.
Now in its new updated and expanded edition, Dynamic Optimization is, more than ever, the optimum choice for graduate and advanced undergraduate courses in economics, mathematical methods in economics and dynamic optimization, management science, mathematics and engineering.
Author(s): Morton I. Kamien and Nancy L. Schwartz.
Series: Advanced textbooks in economics 31
Edition: 2
Publisher: North-Holland
Year: 1991
Language: English
City: Amsterdam, London
Tags: Mathematical optimization, Control theory, Calculus of variations
Preface to the Fourth Printing........xi
Preface to the Second Edition........xiii
Preface to the First Edition........xv
PART I. CALCULUS OF VARIATIONS
Section 1. Introduction........3
Section 2. Example Solved........12
Section 3. Simplest Problem—Euler Equation........14
Section 4. Examples and Interpretations........21
Section 5. Solving the Euler Equation in Special Cases........30
Section 6. Second Order Conditions........41
Section 7. Isoperimetric Problem........47
Section 8. Free End Value........52
Section 9. Free Horizon—Transversality Conditions........57
Section 10. Equality Constrained Endpoint........65
Section 11. Salvage Value........71
Section 12. Inequality Constraint Endpoints and Sensitivity Analysis........77
Section 13. Corners........86
Section 14. Inequality Constraints in (t , x)........90
Section 15. Infinite Horizon Autonomous Problems........95
Section 16. Most Rapid Approach Paths........97
Section 17. Diagrammatic Analysis........102
Section 18. Several Functions and Double Integrals........112
PART II: OPTIMAL CONTROL
Section 1. Introduction........121
Section 2. Simplest Problem—Necessary Conditions........124
Section 3. Sufficiency........133
Section 4. Interpretations........136
Section 5. Several Variables........142
Section 6. Fixed Endpoint Problems........147
Section 7. Various Endpoint Conditions........155
Section 8. Discounting, Current Values, Comparative Dynamics........164
Section 9. Equilibria in Infinite Horizon Autonomous Problems........174
Section 10. Bounded Controls........185
Section 11. Further Control Constraint........195
Section 12. Discontinuous and Bang-Bang Control........202
Section 13. Singular Solutions and Most Rapid Approach Paths........209
Section 14. The Pontryagin Maximum Principle, Existence........218
Section 15. Further Sufficiency Theorems........221
Section 16. Alternative Formulations........227
Section 17. State Variable Inequality Constraints........230
Section 18. Jumps in the State Variable, Switches in State Equations........240
Section 19. Delayed Response........248
Section 20. Optimal Control with Integral State Equations........253
Section 21. Dynamic Programming........259
Section 22. Stochastic Optimal Control........264
Section 23. Differential Games........272
APPENDIX A. CALCULUS AND NONLINEAR PROGRAMMING
Section 1. Calculus Techniques........291
Section 2. Mean-Value Theorems........294
Section 3. Concave and Convex Functions........298
Section 4. Maxima and Minima........303
Section 5. Equality Constrained Optimization........307
Section 6. Inequality Constrained Optimization........313
Section 7. Line Integrals and Green's Theorem........320
APPENDIX B. DIFFERENTIAL EQUATIONS
Section 1. Introduction........325
Section 2. Linear First Order Differential Equations........328
Section 3. Linear Second Order Differential Equations........332
Section 4. Linear nth Order Differential Equations........339
Section 5. A Pair of Linear Equations........344
Section 6. Existence and Uniqueness of Solutions........350
References........353
Author Index........367
Subject Index........371
