Robert Giegerich, Robert Giegerich, Carsten Meyer · 2008
Abstract. Dynamic programming is a classic programming technique, applicable in a wide variety of domains, like stochastic systems analysis, operations research, combinatorics of discrete structures, flow problems, parsing with ambiguous grammars, or biosequence analysis. Yet, no methodology is available for designing such algorithms. The matrix recurrences that typically describe a dynamic programming algorithm are difficult to construct, error-prone to implement, and almost impossible to debug. This article introduces an algebraic style of dynamic programming over sequence data. We define the formal framework including a formalization of Bellman’s principle, specify an executable specification language, and show how algorithm design decisions and tuning for efficiency can be describedonaconvenientlevelofabstraction.
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David B. Wagner
This is the first in a series of columns on advanced programming techniques and algorithms. This issue's column discusses dynamic programming, a powerful algorithmic scheme for solving discrete optimization problems. We illustrate the concepts with the generation of Fibonacci numbers, and then present two nontrivial examples, optimal matrix-chain multiplication and multiple-class mean value analysis of queueing networks. This last example applies the technique to a queueing-theory problem that was solved in a very different way by A.O. Allen and G. Hynes in volume 1, issue 3 of this journal.
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Christopher Rose · Journal of Mathematical Analysis and Applications · 1969
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K. B. Haley · Journal of the Operational Research Society · 1969
"Dynamic Programming of Economic Decisions: Dynamic Programming." Journal of the Operational Research Society, 20(4), pp. 505–506
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Marc Gengler · 2007
e of conditional optimization, the decomposition scheme and so on, before defining the notions of state space, decision space, the transition and objective functions and so on. We also present the mathematical models called sequential or multistage decision models and markovian decision policies. The formal discussion aims at showing how dynamic programming works and what problems can be restated so as to fit into the general framework. It intends to describe the dynamic programming methodology from a more general point of view than just giving the dynamic programming solution for a certain number of more or less trivial problems. Thus, it should give the reader the insight needed to analyze new problems and come up with original solutions. The second part of this chapter is devoted to a certain number of example problems from different application areas showing how standard problems can be solved using dynamic programming. The examples will be selected so as to emphasize the
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Piernicola Bettiol, Richard Vinter · Springer monographs in mathematics · 2023
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Thomas J. Sargent, John Stachurski · Cambridge University Press eBooks · 2025
Dynamic programming (DP) is a sub-field of optimization concerned with sequential decision making over time. The essential ideas of DP have been adopted in many applications, from robotics and AI to the sequencing of DNA. It is used around the world to control aircraft, route shipping, test products, recommend information on media platforms and solve major research problems. Dynamic Programming: Finite States treats the theory of dynamic programming and its applications in economics, finance, and operations research. It contains classical results on dynamic programming as well as extensions created by researchers and practitioners as they wrestle with formulating and solving dynamic models that can explain patterns observed in data. Adopting an abstract framework that provides great generality, this book facilitates rapid progress to the research frontier by combining rigorous theory with numerous applications, many solved exercises, and detailed open-source computer code.
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2017
Dynamic programming is a subset of the “divide and conquer” method, given that a solution to a problem depends on the previous solutions obtained from subproblems. The main and major difference between these two methods lies in the superimposition of subproblems in dynamic programming. It can be claimed that the “divide and conquer” method works by following a top-down approach, whereas dynamic programming follows a bottomup approach. A dynamic programming algorithm generally consists of a number of phases that link together to come to the optimal solution: characterization, definition, calculation and construction. This chapter explores a number of simple examples for which the problem is formulated, and then it applies the principle of optimality to find a solution. Stochastic processes have many applications, particularly for managing transport networks, managing traffic, electric systems, telecommunications, signal processing, filtering, finance, the economy, etc. The chapter also talks about Markov chains.
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Michael Bode, Hedley S. Grantham · 2019
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Palgrave Macmillan eBooks · 2013
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John Rust · The New Palgrave Dictionary of Economics · 2018
This article reviews the history and theory of dynamic programming (DP), a recursive method of solving sequential decision problems under uncertainty. It discusses computational algorithms for the numerical solution of DP problems, and an important limitation in our ability to solve realistic large-scale dynamic programming problems, the ‘curse of dimensionality’. It also summarizes recent research in complexity theory that delineates situations where the curse can be broken (allowing us to solve DPs using fast polynomial time algorithms), and situations where it is insuperable. The literature on econometric estimation and testing of DP models is reviewed, as is another ‘scientific limit to knowledge’, namely, the identification problem.
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William T. Ziemba, Raymond G. Vickson · World Scientific handbook in financial economic series · 2006
AbstractThe following sections are included:Introduction to Dynamic Programming
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William P. Fox · 2020
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Martin H. Weik · 2000
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Ting Chen, Michael S. Waterman · Encyclopedia of Life Sciences · 2005
Abstract Dynamic programming is an optimization technique used in mathematics and computer science. It solves problems by recursively solving the subproblems that have overlapping substructures and then combining the solutions to these subproblems.
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Bellman, Richard, 1920-1984 98062 aut
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James E. Killen · 2021
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Sumru Altuğ, Pamela Labadie · Cambridge University Press eBooks · 2008
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Pierre Borne, Dumitru Popescu, Florin Gh. Filip et al. · 2013
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Wendell H. Fleming, Raymond Rishel · 1975
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