Dynamic programming : foundations and principles

著者

• Sniedovich, Moshe

書誌事項

Dynamic programming : foundations and principles

Moshe Sniedovich

（Monographs and textbooks in pure and applied mathematics, 297）

CRC Press, c2011

2nd ed

• : hardcover

注記

Includes bibliographical references (p. 549-594) and index

内容説明・目次

内容説明

Incorporating a number of the author's recent ideas and examples, Dynamic Programming: Foundations and Principles, Second Edition presents a comprehensive and rigorous treatment of dynamic programming. The author emphasizes the crucial role that modeling plays in understanding this area. He also shows how Dijkstra's algorithm is an excellent example of a dynamic programming algorithm, despite the impression given by the computer science literature. New to the Second Edition Expanded discussions of sequential decision models and the role of the state variable in modeling A new chapter on forward dynamic programming models A new chapter on the Push method that gives a dynamic programming perspective on Dijkstra's algorithm for the shortest path problem A new appendix on the Corridor method Taking into account recent developments in dynamic programming, this edition continues to provide a systematic, formal outline of Bellman's approach to dynamic programming. It looks at dynamic programming as a problem-solving methodology, identifying its constituent components and explaining its theoretical basis for tackling problems.

目次

Introduction Welcome to Dynamic Programming! How to Read This Book SCIENCE Fundamentals Introduction Meta-Recipe Revisited Problem Formulation Decomposition of the Solution Set Principle of Conditional Optimization Conditional Problems Optimality Equation Solution Procedure Time Out: Direct Enumeration! Equivalent Conditional Problems Modified Problems The Role of a Decomposition Scheme Dynamic Programming Problem - Revisited Trivial Decomposition Scheme Summary and a Look Ahead Multistage Decision Model Introduction A Prototype Multistage Decision Model Problem vs Problem Formulation Policies Markovian Policies Remarks on the Notation Summary Bibliographic Notes Dynamic Programming - An Outline Introduction Preliminary Analysis Markovian Decomposition Scheme Optimality Equation Dynamic Programming Problems The Final State Model Principle of Optimality Summary Solution Methods Introduction Additive Functional Equations Truncated Functional Equations Nontruncated Functional Equations Summary Successive Approximation Methods Introduction Motivation Preliminaries Functional Equations of Type One Functional Equations of Type Two Truncation Method Stationary Models Truncation and Successive Approximation Summary Bibliographic Notes Optimal Policies Introduction Preliminary Analysis Truncated Functional Equations Nontruncated Functional Equations Successive Approximation in the Policy Space Summary Bibliographic Notes The Curse of Dimensionality Introduction Motivation Discrete Problems Special Cases Complete Enumeration Conclusions The Rest Is Mathematics and Experience Introduction Choice of Model Dynamic Programming Models Forward Decomposition Models Practice What You Preach! Computational Schemes Applications Dynamic Programming Software Summary ART Refinements Introduction Weak-Markovian Condition Markovian Formulations Decomposition Schemes Sequential Decision Models Example Shortest Path Model The Art of Dynamic Programming Modeling Summary Bibliographic Notes The State Introduction Preliminary Analysis Mathematically Speaking Decomposition Revisited Infeasible States and Decisions State Aggregation Nodes as States Multistage vs Sequential Models Models vs Functional Equations Easy Problems Modeling Tips Concluding Remarks Summary Parametric Schemes Introduction Background and Motivation Fractional Programming Scheme C-Programming Scheme Lagrange Multiplier Scheme Summary Bibliographic Notes The Principle of Optimality Introduction Bellman's Principle of Optimality Prevailing Interpretation Variations on a Theme Criticism So What Is Amiss? The Final State Model Revisited Bellman's Treatment of Dynamic Programming Summary Post Script: Pontryagin's Maximum Principle Forward Decomposition Introduction Function Decomposition Initial Problem Separable Objective Functions Revisited Modified Problems Revisited Backward Conditional Problems Revisited Markovian Condition Revisited Forward Functional Equation Impact on the State Space Anomaly Pathologic Cases Summary and Conclusions Bibliographic Notes Push! Introduction The Pull Method The Push Method Monotone Accumulated Return Processes Dijkstra's Algorithm Summary Bibliographic Notes EPILOGUE What Then Is Dynamic Programming? Review Non-Optimization Problems An Abstract Dynamic Programming Model Examples The Towers of Hanoi Problem Optimization-Free Dynamic Programming Concluding Remarks Appendix A: Contraction Mapping Appendix B: Fractional Programming Appendix C: Composite Concave Programming Appendix D: The Principle of Optimality in Stochastic Processes Appendix E: The Corridor Method Bibliography Index

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BB0337402X
• ISBN:
  • 9780824740993
• LCCN: 2010029350
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Boca Raton
• ページ数/冊数: xiii, 604 p.
• 大きさ: 25 cm
• 分類:
  • LCC : T57.83
  • DC22 : 519.7/03
• 件名:
  • LCSH : Dynamic programming
• 親書誌ID:
  • BA00046446