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基本説明
With over 400 useful references, this edition descusses the dynamic programming analysis of a problem, illustrates the rationale behind this analysis, and clarifies the theoretical grounds that justify the rationale.
Full Description
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 EditionExpanded discussions of sequential decision models and the role of the state variable in modeling A new chapter on forward dynamic programming modelsA new chapter on the Push method that gives a dynamic programming perspective on Dijkstra's algorithm for the shortest path problemA new appendix on the Corridor methodTaking 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.
Contents
IntroductionWelcome to Dynamic Programming! How to Read This BookSCIENCEFundamentalsIntroduction 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 AheadMultistage Decision ModelIntroduction A Prototype Multistage Decision Model Problem vs Problem Formulation Policies Markovian Policies Remarks on the Notation Summary Bibliographic NotesDynamic Programming - An OutlineIntroduction Preliminary Analysis Markovian Decomposition SchemeOptimality Equation Dynamic Programming Problems The Final State Model Principle of Optimality SummarySolution MethodsIntroduction Additive Functional Equations Truncated Functional Equations Nontruncated Functional Equations SummarySuccessive Approximation MethodsIntroduction Motivation Preliminaries Functional Equations of Type One Functional Equations of Type Two Truncation Method Stationary Models Truncation and Successive Approximation Summary Bibliographic NotesOptimal PoliciesIntroduction Preliminary Analysis Truncated Functional Equations Nontruncated Functional Equations Successive Approximation in the Policy Space Summary Bibliographic NotesThe Curse of DimensionalityIntroduction Motivation Discrete Problems Special Cases Complete Enumeration ConclusionsThe Rest Is Mathematics and Experience Introduction Choice of Model Dynamic Programming ModelsForward Decomposition Models Practice What You Preach! Computational Schemes Applications Dynamic Programming Software SummaryARTRefinementsIntroduction Weak-Markovian Condition Markovian Formulations Decomposition Schemes Sequential Decision Models Example Shortest Path Model The Art of Dynamic Programming Modeling Summary Bibliographic NotesThe StateIntroduction 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 SummaryParametric SchemesIntroduction Background and Motivation Fractional Programming Scheme C-Programming Scheme Lagrange Multiplier Scheme Summary Bibliographic NotesThe Principle of OptimalityIntroduction 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 PrincipleForward Decomposition Introduction Function Decomposition Initial Problem Separable Objective Functions RevisitedModified Problems Revisited Backward Conditional Problems Revisited Markovian Condition Revisited Forward Functional Equation Impact on the State SpaceAnomaly Pathologic Cases Summary and Conclusions Bibliographic Notes Push! Introduction The Pull Method The Push Method Monotone Accumulated Return Processes Dijkstra's Algorithm Summary Bibliographic NotesEPILOGUEWhat Then Is Dynamic Programming?Review Non-Optimization Problems An Abstract Dynamic Programming Model Examples The Towers of Hanoi Problem Optimization-Free Dynamic Programming Concluding RemarksAppendix A: Contraction MappingAppendix B: Fractional ProgrammingAppendix C: Composite Concave ProgrammingAppendix D: The Principle of Optimality in Stochastic ProcessesAppendix E: The Corridor MethodBibliographyIndex
