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Introduction to Dynamic Programming
International Series in Modern Applied Mathematics and Computer Science, Volume 1
1st Edition - January 1, 1981
Authors: Leon Cooper, Mary W. Cooper
Editor: E. Y. Rodin
9 7 8 - 1 - 4 8 3 1 - 3 6 6 2 - 2
Introduction to Dynamic Programming introduces the reader to dynamic programming and presents the underlying mathematical ideas and results, as well as the application of these… Read more
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Introduction to Dynamic Programming introduces the reader to dynamic programming and presents the underlying mathematical ideas and results, as well as the application of these ideas to various problem areas. A large number of solved practical problems and computational examples are included to clarify the way dynamic programming is used to solve problems. A consistent notation is applied throughout the text for the expression of quantities such as state variables and decision variables.
This monograph consists of 10 chapters and opens with an overview of dynamic programming as a particular approach to optimization, along with the basic components of any mathematical optimization model. The following chapters discuss the application of dynamic programming to variational problems; functional equations and the principle of optimality; reduction of state dimensionality and approximations; and stochastic processes and the calculus of variations. The final chapter looks at several actual applications of dynamic programming to practical problems, such as animal feedlot optimization and optimal scheduling of excess cash investment.
This book should be suitable for self-study or for use as a text in a one-semester course on dynamic programming at the senior or first-year, graduate level for students of mathematics, statistics, operations research, economics, business, industrial engineering, or other engineering fields.
Chapter 1. Introduction
1.2. Separable Functions
1.3. Convex and Concave Functions
1.4. Optima of Convex and Concave Functions
1.5. Dynamic Programming
1.6. Dynamic Programming: Advantages and Limitations
1.7. The Development of Dynamic Programming
Chapter 2. Some Simple Examples
2.2. The Wandering Applied Mathematician
2.3. The Wandering Applied Mathematician (Continued)
2.4. A Problem in "Division"
2.5. A Simple Equipment Replacement Problem
Chapter 3. Functional Equations: Basic Theory
3.2. Sequential Decision Processes
3.3. Functional Equations and the Principle of Optimality
3.4. The Principle of Optimality—Necessary and Sufficient Conditions