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1

O'Caoimh, C. C., and Moshe Sniedovich. "Dynamic Programming." Mathematical Gazette 77, no. 479 (July 1993): 284. http://dx.doi.org/10.2307/3619755.

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2

Smith, David K., and Moshe Sniedovich. "Dynamic Programming." Journal of the Operational Research Society 44, no. 5 (May 1993): 526. http://dx.doi.org/10.2307/2583920.

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3

Smith, David K. "Dynamic Programming." Journal of the Operational Research Society 44, no. 5 (May 1993): 526–27. http://dx.doi.org/10.1057/jors.1993.90.

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4

Valqui Vidal, RenéVictor. "Dynamic programming." European Journal of Operational Research 71, no. 1 (November 1993): 135–36. http://dx.doi.org/10.1016/0377-2217(93)90270-w.

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5

Jahagirdar, Ashok. "Dynamic Programming vs. Recursive Programming: A Comparative Analysis of Efficiency and Applicability." International Journal of Science and Research (IJSR) 14, no. 2 (February 27, 2025): 1282–84. https://doi.org/10.21275/sr25221083610.

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6

Chow, Gregory C. "Dynamic optimization without dynamic programming." Economic Modelling 9, no. 1 (January 1992): 3–9. http://dx.doi.org/10.1016/0264-9993(92)90002-j.

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7

Kenea, Tadios Kiros. "Solving Shortest Route Using Dynamic Programming Problem." Indian Journal Of Science And Technology 15, no. 31 (August 21, 2022): 1527–31. http://dx.doi.org/10.17485/ijst/v15i31.1342.

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8

Lageweg, B. J., J. K. Lenstra, A. H. G. RinnooyKan, L. Stougie, and A. H. G. Rinnooy Kan. "STOCHASTIC INTEGER PROGRAMMING BY DYNAMIC PROGRAMMING." Statistica Neerlandica 39, no. 2 (June 1985): 97–113. http://dx.doi.org/10.1111/j.1467-9574.1985.tb01131.x.

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9

Iwamoto, S. "From Dynamic Programming to Bynamic Programming." Journal of Mathematical Analysis and Applications 177, no. 1 (July 1993): 56–74. http://dx.doi.org/10.1006/jmaa.1993.1243.

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10

Kaur, Kamaljeet, and Neeti Taneja. "Dynamic Programming: LCS." International Journal of Advanced Research in Computer Science and Software Engineering 7, no. 6 (June 30, 2017): 272–77. http://dx.doi.org/10.23956/ijarcsse/v7i6/0131.

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Jdid, Maissam, and Rafif Alhabib. "Neutrosophical dynamic programming." International Journal of Neutrosophic Science 18, no. 3 (2022): 157–65. http://dx.doi.org/10.54216/ijns.1803013.

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Abstract (sommario):
The great development that science has witnessed in all fields has reduced the risks and losses resulting from undertaking any business or projects. Since the emergence of the science of operations research, many life issues have been addressed by relying on it, and by using its methods, we have been able to establish projects and businesses and use the available capabilities in an ideal manner. Which achieved great success in all areas and reduced the losses of all kinds, whether material or human, that we were exposed to because of carrying out these works or projects without prior study. We are now able to model, analyze and solve a wide range of problems that can be broken down into a set of partial problems using dynamic programming. Programming that is used to find the optimal solution in a multi-step situation that involves a set of related decisions. In this research, we study one of the operations research problems that are solved using dynamic programming. It is the problem of creating an expressway between two cities, using the neutrosophic logic. The logic that takes into account all the specific and non-specific data and takes into account all the circumstances that can face us during the implementation of the project. The goal of studying this issue is to determine the optimal total cost, which is related to the partial costs presented by the study prepared for this project. In order to avoid losses we will take the partial costs neutrosophic values of the form , where represents the minimum partial cost in stage and represents the upper limit of the partial cost in stage . Through the indeterminacy offered by neutrosophic logic, we are able to find the ideal solution that will bring us the lowest possible cost for constructing this expressway. It takes into account all the circumstances that may encounter us in our study, and we will present an applied example that illustrates the study.
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12

Iwamoto, Seiichi. "PRIMITIVE DYNAMIC PROGRAMMING." Bulletin of informatics and cybernetics 36 (December 2004): 163–72. http://dx.doi.org/10.5109/12585.

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13

Tsoi, Aleksander Alekseievitch. "Recurrent dynamic programming." Ciência e Natura 22, no. 22 (December 11, 2000): 07. http://dx.doi.org/10.5902/2179460x27025.

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We developed the tchniques for immediate solution and optimization by parts for discrete nonlinear separable programming problem on the graph. These two techniques are based on the use of the dynamic programming method that results in obtaining one algorithm of dynamic programming built into another one. The both techniques make use of the graph structure. Multiple use of the decomposition is generalized in the frames of the hierarchically recurrent algorithm of dynamic programming.
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14

Lincoln, B., and A. Rantzer. "Relaxing Dynamic Programming." IEEE Transactions on Automatic Control 51, no. 8 (August 2006): 1249–60. http://dx.doi.org/10.1109/tac.2006.878720.

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15

Huang, S. H. S., Hongfei Liu, and V. Viswanathan. "Parallel dynamic programming." IEEE Transactions on Parallel and Distributed Systems 5, no. 3 (March 1994): 326–28. http://dx.doi.org/10.1109/71.277784.

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16

Murray, J. J., C. J. Cox, G. G. Lendaris, and R. Saeks. "Adaptive dynamic programming." IEEE Transactions on Systems, Man and Cybernetics, Part C (Applications and Reviews) 32, no. 2 (May 2002): 140–53. http://dx.doi.org/10.1109/tsmcc.2002.801727.

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17

Kossmann, Donald, and Konrad Stocker. "Iterative dynamic programming." ACM Transactions on Database Systems 25, no. 1 (March 2000): 43–82. http://dx.doi.org/10.1145/352958.352982.

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18

Haskell, William B., Rahul Jain, and Dileep Kalathil. "Empirical Dynamic Programming." Mathematics of Operations Research 41, no. 2 (May 2016): 402–29. http://dx.doi.org/10.1287/moor.2015.0733.

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19

Bender, Christian, Christian Gärtner, and Nikolaus Schweizer. "Pathwise Dynamic Programming." Mathematics of Operations Research 43, no. 3 (August 2018): 965–95. http://dx.doi.org/10.1287/moor.2017.0891.

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20

Chudoung, Jerawan. "Iterative dynamic programming." Automatica 39, no. 7 (July 2003): 1315–16. http://dx.doi.org/10.1016/s0005-1098(03)00079-7.

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21

Caminiti, Saverio, Irene Finocchi, Emanuele G. Fusco, and Francesco Silvestri. "Resilient Dynamic Programming." Algorithmica 77, no. 2 (October 13, 2015): 389–425. http://dx.doi.org/10.1007/s00453-015-0073-z.

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22

Iyengar, Garud N. "Robust Dynamic Programming." Mathematics of Operations Research 30, no. 2 (May 2005): 257–80. http://dx.doi.org/10.1287/moor.1040.0129.

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23

Pardalos, Panos M. "Abstract dynamic programming." Optimization Methods and Software 29, no. 3 (November 20, 2013): 671–72. http://dx.doi.org/10.1080/10556788.2013.858876.

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24

van Otterlo, Martijn. "Intensional dynamic programming. A Rosetta stone for structured dynamic programming." Journal of Algorithms 64, no. 4 (October 2009): 169–91. http://dx.doi.org/10.1016/j.jalgor.2009.04.004.

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25

Cai, Yongyang, Kenneth L. Judd, Thomas S. Lontzek, Valentina Michelangeli, and Che-Lin Su. "A NONLINEAR PROGRAMMING METHOD FOR DYNAMIC PROGRAMMING." Macroeconomic Dynamics 21, no. 2 (January 18, 2016): 336–61. http://dx.doi.org/10.1017/s1365100515000528.

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Abstract (sommario):
A nonlinear programming formulation is introduced to solve infinite-horizon dynamic programming problems. This extends the linear approach to dynamic programming by using ideas from approximation theory to approximate value functions. Our numerical results show that this nonlinear programming is efficient and accurate, and avoids inefficient discretization.
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26

Travers, D. L., and R. J. Kaye. "Dynamic dispatch by constructive dynamic programming." IEEE Transactions on Power Systems 13, no. 1 (1998): 72–78. http://dx.doi.org/10.1109/59.651616.

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27

Karpov, D. A., and V. I. Struchenkov. "EFFECTIVE DYNAMIC PROGRAMMING ALGORITHMS." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 194 (August 2020): 3–11. http://dx.doi.org/10.14489/vkit.2020.08.pp.003-011.

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Abstract (sommario):
This article is devoted to the analysis of the possibilities of increasing the speed of dynamic programming algorithms in solving applied problems of large dimension. Dynamic programming is considered rather than as an optimization method, but as a methodology that allows developing, from a single theoretical point of view, algorithms for solving problems that can be formalized in the form of multi-stage (multi-step) processes in which similar tasks are solved at all steps. It is shown that traditional dynamic programming algorithms based on preliminary setting of a regular grid of states are ineffective, especially if the parameters defining the states are not integer. The problems are considered, in the solution of which it is advisable to build a set of states in the process of counting, moving from one stage to another. Additional conditions are formulated that must be satisfied by the problem so that deliberately hopeless states do not fall into sets of states at each step. This ensures the rejection of not only the paths leading to each of the states, as in traditional dynamic programming algorithms, but also the unpromising states themselves, which greatly increases the efficiency of dynamic programming. Examples of applied problems are given, for the solution of which traditional dynamic programming algorithms were previously proposed, but which can be more efficiently solved by the proposed algorithm with state rejection. As applied to two-parameter problems, the concrete examples demonstrate the effectiveness of the algorithm with rejecting states in comparison with traditional algorithms, especially with increasing the dimension of the problem. An applied problem is considered, in the solution of which dynamic programming is used to construct recurrent formulas for calculating the optimal solution without enumerating options at all.
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28

Smith, Peter. "Dynamic Programming in Action." Journal of the Operational Research Society 40, no. 9 (September 1989): 779. http://dx.doi.org/10.2307/2583059.

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29

Hisano, Hiroshi. "ON NONDETERMINISTIC DYNAMIC PROGRAMMING." Bulletin of informatics and cybernetics 40 (December 2008): 1–15. http://dx.doi.org/10.5109/18991.

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30

Eddy, Sean R. "What is dynamic programming?" Nature Biotechnology 22, no. 7 (July 2004): 909–10. http://dx.doi.org/10.1038/nbt0704-909.

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31

Karpov, D. A., and V. I. Struchenkov. "EFFECTIVE DYNAMIC PROGRAMMING ALGORITHMS." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 194 (August 2020): 3–11. http://dx.doi.org/10.14489/vkit.2020.08.pp.003-011.

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Abstract (sommario):
This article is devoted to the analysis of the possibilities of increasing the speed of dynamic programming algorithms in solving applied problems of large dimension. Dynamic programming is considered rather than as an optimization method, but as a methodology that allows developing, from a single theoretical point of view, algorithms for solving problems that can be formalized in the form of multi-stage (multi-step) processes in which similar tasks are solved at all steps. It is shown that traditional dynamic programming algorithms based on preliminary setting of a regular grid of states are ineffective, especially if the parameters defining the states are not integer. The problems are considered, in the solution of which it is advisable to build a set of states in the process of counting, moving from one stage to another. Additional conditions are formulated that must be satisfied by the problem so that deliberately hopeless states do not fall into sets of states at each step. This ensures the rejection of not only the paths leading to each of the states, as in traditional dynamic programming algorithms, but also the unpromising states themselves, which greatly increases the efficiency of dynamic programming. Examples of applied problems are given, for the solution of which traditional dynamic programming algorithms were previously proposed, but which can be more efficiently solved by the proposed algorithm with state rejection. As applied to two-parameter problems, the concrete examples demonstrate the effectiveness of the algorithm with rejecting states in comparison with traditional algorithms, especially with increasing the dimension of the problem. An applied problem is considered, in the solution of which dynamic programming is used to construct recurrent formulas for calculating the optimal solution without enumerating options at all.
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32

HOLMES, IAN, and RICHARD DURBIN. "Dynamic Programming Alignment Accuracy." Journal of Computational Biology 5, no. 3 (January 1998): 493–504. http://dx.doi.org/10.1089/cmb.1998.5.493.

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33

Bean, James C., John R. Birge, and Robert L. Smith. "Aggregation in Dynamic Programming." Operations Research 35, no. 2 (April 1987): 215–20. http://dx.doi.org/10.1287/opre.35.2.215.

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34

Kindermann, S., and A. Leitão. "Regularization by dynamic programming." Journal of Inverse and Ill-posed Problems 15, no. 3 (June 2007): 295–310. http://dx.doi.org/10.1515/jiip.2007.016.

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35

Georghiou, Angelos, Angelos Tsoukalas, and Wolfram Wiesemann. "Robust Dual Dynamic Programming." Operations Research 67, no. 3 (May 2019): 813–30. http://dx.doi.org/10.1287/opre.2018.1835.

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36

Nowakowski, Andrzej. "The dual dynamic programming." Proceedings of the American Mathematical Society 116, no. 4 (April 1, 1992): 1089. http://dx.doi.org/10.1090/s0002-9939-1992-1102860-3.

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37

Smith, Peter. "Dynamic Programming in Action." Journal of the Operational Research Society 40, no. 9 (September 1989): 779–87. http://dx.doi.org/10.1057/jors.1989.140.

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38

Sudderth, William D. "Finitely Additive Dynamic Programming." Mathematics of Operations Research 41, no. 1 (February 2016): 92–108. http://dx.doi.org/10.1287/moor.2015.0717.

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39

Feinberg, Eugene A., and Adam Shwartz. "Constrained Discounted Dynamic Programming." Mathematics of Operations Research 21, no. 4 (November 1996): 922–45. http://dx.doi.org/10.1287/moor.21.4.922.

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40

Madievski, Anton G., and John B. Moore. "On Robust Dynamic Programming." IFAC Proceedings Volumes 29, no. 1 (June 1996): 1715–20. http://dx.doi.org/10.1016/s1474-6670(17)57916-1.

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41

de Madrid, A. P., S. Dormido, F. Morilla, and L. Grau. "Dynamic Programming Predictive Control." IFAC Proceedings Volumes 29, no. 1 (June 1996): 1721–26. http://dx.doi.org/10.1016/s1474-6670(17)57917-3.

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42

Wu, Cang-pu. "Multicriteria Differential Dynamic Programming." IFAC Proceedings Volumes 20, no. 9 (August 1987): 431–36. http://dx.doi.org/10.1016/s1474-6670(17)55744-4.

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43

Deisenroth, Marc Peter, Carl Edward Rasmussen, and Jan Peters. "Gaussian process dynamic programming." Neurocomputing 72, no. 7-9 (March 2009): 1508–24. http://dx.doi.org/10.1016/j.neucom.2008.12.019.

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44

Poch, Leslie A., and R. T. Jenkins. "4.4. Dynamic programming models." Energy 15, no. 7-8 (July 1990): 573–81. http://dx.doi.org/10.1016/0360-5442(90)90006-n.

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45

Galewska, E., and A. Nowakowski. "Multidimensional Dual Dynamic Programming." Journal of Optimization Theory and Applications 124, no. 1 (January 2005): 175–86. http://dx.doi.org/10.1007/s10957-004-6471-z.

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46

Wang, Chung-lie. "Dynamic programming and inequalities." Journal of Mathematical Analysis and Applications 150, no. 2 (August 1990): 528–50. http://dx.doi.org/10.1016/0022-247x(90)90121-u.

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47

Cotter, Kevin D., and Jee-Hyeong Park. "Non-concave dynamic programming." Economics Letters 90, no. 1 (January 2006): 141–46. http://dx.doi.org/10.1016/j.econlet.2005.07.018.

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48

Cai, Yongyang, and Kenneth L. Judd. "Shape-preserving dynamic programming." Mathematical Methods of Operations Research 77, no. 3 (September 9, 2012): 407–21. http://dx.doi.org/10.1007/s00186-012-0406-5.

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49

Jalali, A., and M. J. Ferguson. "On distributed dynamic programming." IEEE Transactions on Automatic Control 37, no. 5 (May 1992): 685–89. http://dx.doi.org/10.1109/9.135517.

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50

ASANO, TAKAO. "DYNAMIC PROGRAMMING ON INTERVALS." International Journal of Computational Geometry & Applications 03, no. 03 (September 1993): 323–30. http://dx.doi.org/10.1142/s0218195993000208.

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Abstract (sommario):
We consider problems on intervals which can be solved by dynamic programming. Specifically, we give an efficient implementation of dynamic programming on intervals. As an application, an optimal sequential partition of a graph G=(V, E) can be obtained in O(m log n) time, where n=|V| and m=|E|. We also present an O(n log n) time algorithm for finding a minimum weight dominating set of an interval graph G=(V, E), and an O(m log n) time algorithm for finding a maximum weight clique of a circular-arc graph G=(V, E), provided their intersection models of n intervals (arcs) are given.
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