Programming, discrete dynamic

In general, dynamic programming is an algorithmic scheme for solving discrete optimisation problems that have overlapping subproblems. In a dynamic... 

The discrete merge method is a special case of dynamic programming applied to branch list processing. It is applicable to a wide class of network... 

C Discrete Dynamic Programming An Introduction to the Optimization of Staged Processes. New York Blaisdell, 1964. 

R. Aris. Discrete Dynamic Programming. Blaisdell, New York, 1964. 

Discrete Dynamic Programming, Blaisdell Press, New York, 1964, S. E. Dreyfus and A. M. Law, The Art and Theory of Dynamic Programming, Academic Press, New York, 1977 and T. F. Edgar and D. M. Kmmelblau, Optimization of Chemical Processes, McGraw-Hill Book Company, New York, 1988. 

Bellman (1957) has suggested that the equation may be integrated by a finite difference technique ( Dynamic Programming, p. 254), but he acknowledges the likelihood of computational difficulties and is led to formulate a discrete version of the problem. Fortunately, in the case we shall be concerned with the method of characteristics is well suited to the integration of these equations. 

Tabular method of discrete optimization. The basis of dynamic programming is the principle of prefix optimality. This principle states that the optimal solution to the optimization problem can be composed of optimal solutions of a limited number of smaller instances of the same type of problem. The tabular method incrementally solves subinstances of increas-... 

Li, D., and Haimes, Y. Y. (1989), Multiobjective Dynamic Programming The State of the Art, Control Theory and Advanced Technology, SpecM Issue on Multiobjective Discrete Dynamic System Control Theory and Advanced Technology, Y. Y. Haimes and D. Li, Eds., Vol. 5, pp. 

The state space S can be a finite, countably infinite, or uncountable set. This article addresses dynamic programs with finite or countably infinite, also called discrete, state spaces S. 

The dynamic process changes from state to state over time. The transitions between states may be deterministic or random. The presentation here is for a dynamic program with discrete time parameter r = 0, 1,. . . , and with random transitions. 

Bertsekas, D. P. (1975), Convergence of Discretization Procedures in Dynamic Programming, /FEE Transactions on Automatic Control, Vol. AC-20, pp. 415-419. 

Chang, C. S. (1966), Discrete-Sample Curve Fitting Using Chebyshev Polynomials and the Approximate Determination of Optimal Trajectories via Dynamic Programming, IEEE Transactions on Automatic Control, Vol. AC-11, pp. 116-118. 

Hinderer, K. (1970), Foundations of Non-stationary Dynamic Programming with Discrete Time Parameter. Springer, Berlin. 

Aris, R., The Optimal Design of Chemical Reactors—A Study in Dynamic Programming, Academic Press, New York, 1961 Discrete Dynamic Programming, Blaisdell, Mass, 1964 Introduction to the Analysis of Chemical Reactors, Prentice-Hall, Englewood Cliffs, N.J., 1965 Elementary Chemical Reactor Analysis, McGraw-Hill, New York, 1969 In Frontiers in Chemical Reaction Engineering (Eds. Doraiswamy, L.K. and Mashelkar, R.A.), Wiley Eastern, New Delhi, India (1984). 

A numerical technique that has become very popular in the control field for optimization of dynamic problems is the IDP (iterative dynamic programming) technique. For application of the IDP procedure, the dynamic trajectory is divided first into NS piecewise constant discrete trajectories. Then, the Bellman s theory of dynamic programming [175] is used to divide the optimization problem into NS smaller optimization problems, which are solved iteratively backwards from the desired target values to the initial conditions. Both SQP and RSA can be used for optimization of the NS smaller optimization problems. IDP has been used for computation of optimum solutions in different problems for different purposes. For example, it was used to minimize energy consumption and byproduct formation in poly(ethylene terephthalate) processes [ 176]. It was also used to develop optimum feed rate policies for the simultaneous control of copolymer composition and MWDs in emulsion reactions [36, 37]. 

The optimal control problem represents one of the most difficult optimization problems as it involves determination of optimal variables, which are vectors. There are three methods to solve these problems, namely, calculus of variation, which results in second-order differential equations, maximum principle, which adds adjoint variables and adjoint equations, and dynamic programming, which involves partial differential equations. For details of these methods, please refer to [23]. If we can discretize the whole system or use the model as a black box, then we can use NLP techniques. However, this results in discontinuous profiles. Since we need to manipulate the techno-socio-economic poHcy, we can consider the intermediate and integrated model for this purpose as it includes economics in the sustainabiHty models. As stated earlier, when we study the increase in per capita consumption, the system becomes unsustainable. Here we present the derivation of techno-socio-economic poHcies using optimal control appHed to the two models. 

Timp and Karssemeijer (2004) proposed an automatic segmentation method based on dynamic programming for lesion segmentation, and achieved valuable results in comparison to discrete contour model and region growing. 

DDLab is an interactive graphics program for studying many different kinds of discrete dynamical systems. Arbitrary architectures can be defined, ranging from Id, 2d or 3d CA to random Boolean networks. 

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