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HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 459New Approach for the Continuing Dynamic...

New Approach for the Continuing Dynamic Programming

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Abstract:

The paper proposes the discrete approximate iteration method to solve single-dimensional continuing dynamic programming model. The paper also presents a comparison of the discrete approximate iteration method and bi- convergent method to solve multi-dimensional continuing dynamic programming model. The algorithm is the following: Firstly, let state value of one of state equations be unknown and the others be known. Secondly, use discrete approximate iteration method to find the optimal value of the unknown state values, continue iterating until all state equations have found optimal values. If the objective function is convex, the algorithm is proved linear convergent. If the objective function is non-concave and non-convex, the algorithm is proved convergent.

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Advanced Research on Industry, Information System and Material Engineering, IISME2012

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Periodical:

Advanced Materials Research (Volume 459)

Pages:

575-578

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.459.575

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Online since:

January 2012

Authors:

Peng Zhang, Xiang Huan Meng

Keywords:

Bi-Convergent Method, Dimension, Discrete Approximate Iteration, Dynamic Programming

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© 2012 Trans Tech Publications Ltd. All Rights Reserved

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[1] R. Bellman . Dynamic programming [M]. Princeton University Press, Princeton, (1957).

[2] Qin Yuyuan. Discrete dynamic programming and Bellman algebra [M]. Science Press, 2009. (in Chinese).

[3] Bernd Heidergott, Geert Jan Olsder, Jacob Van der Woude. Max Plus at Work—Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and its Applications [M]. Princeton University Press, (2006).

DOI: 10.1515/9781400865239

[4] S. Senthil Kumar, V. Palanisamy. A dynamic programming based fast computation Hopfield neural network for unit commitment and economic dispatch [J]. Electric Power Systems Research, 2007, 77: 917–925.

DOI: 10.1016/j.epsr.2006.08.005

[5] S. Sitarz. Hybrid methods in multi-criteria dynamic programming [J], Applied Mathematics and Computation, 2006, 180: 38–45.

DOI: 10.1016/j.amc.2005.11.164

[6] Trzaskalik T., Sitarz S.,. Discrete dynamic programming with outcomes in random variable structures [J]. European Journal of Operational Research, 2007, 177 (3): 1535-1548.

DOI: 10.1016/j.ejor.2005.10.019

[7] Sitarz S. Ant algorithms and simulated annealing for multicriteria dynamic programming [J]. Computers & Operations Research, 2007: 1-14.

DOI: 10.1016/j.cor.2007.09.011

[8] K. Ohno. Differential dynamic programming and separable programs [J]. Journal of Optimization Theory and Applications, 1978, 24 (4): 617-637.

DOI: 10.1007/bf00935303

[9] B. Villarreal , M. H. Karwan. Multicriteria integer programming: a (hybrid) dynamic programming recursive approach [J]. Mathematical programming, 1981, 21: 204-223.

DOI: 10.1007/bf01584241

[10] C. R. Philbrick, Jr, P. K. Kitanidis. Improved dynamic programming methods for optimal control of lumped-paramter stochastic system [J]. Operations Research, 2001, 49 (3): 398-412.

DOI: 10.1287/opre.49.3.398.11219

[11] D. Bertsimas, R. Demir. An approximate dynamic programming approach to multidimensional knapsack problems [J]. Management Science, 2002, 48 (4): 550-565.

DOI: 10.1287/mnsc.48.4.550.208

[12] D. P. De Farias, B. Van Roy. The linear programming approach to approximate dynamic programming [J]. Operations Research, 2003, 51 (6): 850–865.

DOI: 10.1287/opre.51.6.850.24925

[13] M.A. Abo-Sinna. Multiple objective (fuzzy) dynamic programming problems: a survey and some applications [J]. Applied Mathematics and Computation, 2004, 157: 861-888.

DOI: 10.1016/j.amc.2003.08.083

[14] Dengfeng LI, Chuntian Cheng. Stability on multiobjective dynamic programming problems with fuzzy parameters in the objective functions and in the constraints [J]. European Journal of Operational research, 2004, 158: 678-696.

DOI: 10.1016/s0377-2217(03)00374-6

[15] Xu Fu-xia. Decomposable algorithm for large dynamic programming [J]. Chin. Quart.J. of Math., 2007, 22(2): 220-224.

[16] Yuping Wang, Chuangyin Dang. An evolutionary algorithm for dynamic multi-objective optimization [J]. Applied Mathematics and Computation, 2008, 25: 6-18.

DOI: 10.1016/j.amc.2008.05.151

[17] B.T. Kien etc. Subgradient of value functions in parametric dynamic programming [J]. European Journal of Operational research, 2009, 193: 12-22.

[18] Zhang Peng, The research On the Multiperiod M-SV Portfolio Selection Optimization by Discrete approximate iteration [J]. Economic Mathematics, 2008, 3: 257-264. (in Chinese).