Introduction to Dynamic Programming

International Series in Modern Applied Mathematics and Computer Science, Volume 1

Leon Cooper, Mary W. Cooper, E. Y. Rodin

• Publisher: Pergamon
• Year: 2016
• Print ISBN:
  9780080250649
• eBook ISBN:
  9781483136622
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

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.

Table of contents

• Front Cover
• Introduction to Dynamic Programming
• Copyright Page
• Table of Contents
• Preface
• Cliapter 1. Introduction
• Exercises—Chapter 1
• Chapter 2. Some Simple Examples
• Exercises—Chapter 2
• Chapter 3. Functional Equations: Basic Theory
• Exercise—Chapter 3
• Chapter 4. One-dimensional Dynamic Programming: Analytic Solutions
• Exercises—Chapter 4
• Chapter 5. One-dimensional Dynamic Programming: Computational Solutions
• Exercises—Chapter 5
• Chapter 6. Multidimensional Problems
• Exercises—Chapter 6
• Chapter 7. Reduction of State Dimensionality and Approximations
• Exercises—Chapter 7
• Chapter 8. Stochastic Processes and Dynamic Programming
• Exercises—Chapter 8
• Chapter 9. Dynamic Programming and the Calculus of Variations
• Exercises—Chapter 9
• Chapter 10. Applications of Dynamic Programming
• Appendix: Sets, Convexity, and n-Dimensional Geometry
• References
• Index