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IntroductionWelcome to Dynamic Programming! How to Read This Book SCIENCEFundamentalsIntroduction 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 ModelIntroduction A Prototype Multistage Decision Model Problem vs Problem Formulation Policies Markovian Policies Remarks on the Notation Summary Bibliographic Notes Dynamic Programming — An OutlineIntroduction Preliminary Analysis Markovian Decomposition SchemeOptimality Equation Dynamic Programming Problems The Final State Model Principle of Optimality Summary Solution MethodsIntroduction Additive Functional Equations Truncated Functional Equations Nontruncated Functional Equations Summary Successive Approximation MethodsIntroduction Motivation Preliminaries Functional Equations of Type One Functional Equations of Type Two Truncation Method Stationary Models Truncation and Successive Approximation Summary Bibliographic Notes Optimal PoliciesIntroduction Preliminary Analysis Truncated Functional Equations Nontruncated Functional Equations Successive Approximation in the Policy Space Summary Bibliographic Notes The Curse of DimensionalityIntroduction Motivation Discrete Problems Special Cases Complete Enumeration Conclusions The Rest Is Mathematics and Experience Introduction Choice of Model Dynamic Programming ModelsForward Decomposition Models Practice What You Preach! Computational Schemes Applications Dynamic Programming Software Summary ARTRefinementsIntroduction Weak-Markovian Condition Markovian Formulations Decomposition Schemes Sequential Decision Models Example Shortest Path Model The Art of Dynamic Programming Modeling Summary Bibliographic Notes The 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 Summary Parametric SchemesIntroduction Background and Motivation Fractional Programming Scheme C-Programming Scheme Lagrange Multiplier Scheme Summary Bibliographic Notes The 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 Principle Forward 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 Notes EPILOGUEWhat 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 MappingAppendix B: Fractional ProgrammingAppendix C: Composite Concave ProgrammingAppendix D: The Principle of Optimality in Stochastic ProcessesAppendix E: The Corridor Method Bibliography Index