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http://worldcat.org/entity/work/id/365186123

Dynamic programming, generalized states, and switching systems

In this paper it is shown that a combination of the classical Lagrange multiplier formalism and the functional equation technique of dynamic programming enables a number of types of variational problems involving the computation and tabulation of functions of M variables to be treated by computing first sequences of functions of K variables, and then sequences of functions of M--K variables, where K may be chosen within the range 1 <or = K <or = M-1. The choice of K depends upon the process This reduction in the dimensionality of the functions involved is equivalent to an increase in the capability of modern digital computers as far as dynamic programming processes are concerned. (Author).

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  • "Project RAND"@en
  • "Dynamic programming"

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  • "In this paper it is shown that a combination of the classical Lagrange multiplier formalism and the functional equation technique of dynamic programming enables a number of types of variational problems involving the computation and tabulation of functions of M variables to be treated by computing first sequences of functions of K variables, and then sequences of functions of M--K variables, where K may be chosen within the range 1 <or = K <or = M-1. The choice of K depends upon the process This reduction in the dimensionality of the functions involved is equivalent to an increase in the capability of modern digital computers as far as dynamic programming processes are concerned. (Author)."@en
  • "Some applications are given of the functional equation technique of dynamic programming to the treatment of some quadratic variational problems and the linear equations arising therefrom."@en
  • "Dynamic programming, successive approximations, extrapolation, and smoothing are used to treat ill-conditioned systems. Numerical examples are given. (Author)."@en
  • "In this memorandum the author employs the mathematical technique of dynamic programming to obtain a best-fit approximation to a function that is defined over some given interval. He then describes how this method offers an approach to the handling of a certain type of pattern-recognition problem and to the approximation of optimal control policies. (Author)."@en
  • "The object of the paper is to show that a blend of dynamic programming, successive approximations and digital computers enables one to approach various classallasses of nonlinear variational problems formerly far beyond reach."@en
  • "The functional equation technique of dynamic programming is applied to the study of quadratic functionals whose Euler variational equations are linear self-adjoint partial differential equations of the second order. A first consequence is the classical Hadamard variational formula for the Green's function of a region. Some extensions are indicated. (Author)."@en
  • "A multi-stage allocation process; A stochastic multi-stage decision process; The structure of dynamic programming processes; Existence and uniqueness theorems; The optimal inventory equation; Bottleneck problems in multi-stage production processes; Bottleneck problems; A continuous stochastic decision process; A new formalism in the calculus of variations; Multi-stages games; Markovian decision processes."
  • "The usual dynamic programming approach to inventory processes with delays in delivery leads to functions of many variables. This multi-dimensionality prevents the straightforward utilization of digital computers. Using a type of transformation previously applied in the study of engineering control processes, it is shown that a class of inventory processes with time lags can be treated in terms of sequences of functions of one variable, regardless of the length of the delay. (Author)."@en
  • "The paper, shows that the functional equation technique introduced in previous works may be used to provide a new approach to some classical problems in the calculus of variations. In addition to furnishing a new analytic weapon, the method has great potentialities as a computational tool."@en
  • "The mathematical problem is that of minimizing the distilling plant size for an m-cascade process."@en
  • "In this paper, an alternative formulation is presented in dynamic programming terms which is independent of the dimension of x, the state vector. It is based upon an extension of the concept of state variable and has application to a number of systems with switching characteristics. In its simplest form, the approach was used in the study of adaptive control processes."@en
  • "The paper is a summary of some applications of the theory of dynamic programming to various classes of multi-stage decision problems of stochastic type. (Author)."@en
  • "Aspects of problem formulation and problem solution are discussed. In particular, the relevance of these matters to the field of intelligent machines and some connections with the theory and application of dynamic programming are treated. The practical application of scientific philosophy as a technique to guide research and to avoid undue waste of time, energy, and talent is developed. (Author)."@en
  • "Some general sequential estimation and sequential detection processes are provided with an analytical formulation through use of the functional equation technique of dynamic programming. Some reductions which are useful from the computational viewpoint are indicated, and several applications to radar and communication system theory are sketched. (Author)."@en
  • "It is shown that the functional equation technique of the theory of dynamic programming may be used to derive functional differential equations for the characteristic values of a certain integral equation similar to those obtained for the eigenvalues of differential equations. (Author)."@en
  • "The fundu=onal equation technique of dynamic programming is applied to the study of co trol processes governed by equ tions of quite general type. Of particular interest are processes with time lags (differential-difference equations) and processes with distributed parameters (partial differential equations). (Author)."@en
  • "The intensive study in recent years of a variety of descriptive and variational processes, such as those which arise in biology, psychology, engineering, and economics, has uncovered many problems which are too complex to be solved by classical mathematical techniques. In order to describe some of the difficulties involved, the essentials of the classical approach for dealing with processes of this sort, in which there is insufficient information about the state variables, are reviewed. Some of the ways in which dynamic programming and adaptive control may be used to bridge the gap between classical and modern theories are indicated. Problems encountered in the study of adaptive processes are discussed and some directions for future research are suggested. (Author)."@en
  • "A nonlinear two-point boundary value problem arising from a variational context is considered from several points of view. First a direct computational solution via quasilinearization is discussed. This method is quadratically convergent. Then the boundary value problem is converted into an initial value problem using dynamic programming and invariant imbedding. Some aspects of combining the methods in a single calculation are discussed. This gives rise to attractive predictor-corrector integration schemes. In addition, an alternative to the usual Hamilton-Jacobi integration theory for the integration of the Euler equation is given. (Author)."@en
  • "It is shown how the functional equation technique of dynamic programming may be used to obtain a new computational and analytic approach to variational problems. The limited memory capacity of present-day digital computers limits the successful application of these techniques to first and second order systems at the moment, with limited application to higher order systems."@en
  • "A simple, readily applicable technique, requiring no mathematical background beyond elementary calculus, which can be used to compute the solution of a variety of problems in a routine fashion, with no regard to linear or nonlinear, stochastic or deterministic features of the underlying processes is present. (Author)."@en
  • "The application is considered of the theory of dynamic programming to a discrete form of the linear prediction problem, that of minimizing over u sub k a given quadratic form."@en
  • "This bibliography is divided into three parts: first, there is a chronological ordering of publications, with authors listed alphabetically under each year; second, an alphabetical index of authors; third, a subject index, with authors listed alphabetically under each subject category. The subject index includes; allocation processes, calculus of variations, communications and information theory, control processes, equipment replacement and inventory theory, game theory, maximization and minimization, multistage production and scheduling theory, optimal routing and trajectory theory, mathematical physics, reliability, search processes, sequential analysis, transportation processes, stochastic variational processes, adaptive processes, analytic results, computational aspects and surveys."@en
  • "An introduction to the mathematical theory of multistage decision processes, this text takes a functional equation approach to the discovery of optimum policies. The text examines existence and uniqueness theorems, the optimal inventory equation, bottleneck problems in multistage production processes, a new formalism in the calculus of variation, multistage games, and more. 1957 edition. Includes 37 figures."
  • "This paper shows that a combination of dynamic programming gng and the classical meththod of successive approximations permits a systemattic study of various classes of combinatorial problems arising in scheduling theory, communication theory and network theory. Although the method cannot guarantee convergence to the actual solution, it furnishes a monotonic sequence of approximations by means of approximation in policy space. An important feature of the method is the use of the solution of sub-problems of considerable magnitude as steps in the approximation procedure. With the aid of digital computers and the techniques of dynamic programming, this is a feasible method. The HitchcockKoopmans transportation problem, an allocation problem, and the travelling salesman problem are discussed. (Author)."@en
  • "The purpose of this paper is to discuss some variational problems arising from mathematical economics, and some of the methods that can be used to treat these questions both analytically and computationally. The discussion is limited to important and interesting classes of processes, allocation and smoothing processes, and to a discussion of the application of the theory of dynamic programming to those processes. (Author)."@en
  • "This paper indicates how a class of control processes requiring multi-dimensional sequences of functions when treated by the direct methods of dynamic programming can, by means of a transformation familiar to the theory of linear functional equations of differential, difference, or differential-difference type, be reduced to problems involving sequences of functions of one variable in a number of cases, and sequences of functions of two variables in others. These results open the door to a systematic study of nonlinear control processes, with or without time-lags and other types of hereditary behavior, by way of the method of successive approximations."@en
  • "This is a brief description of decision processes in dynamic programming."@en
  • "Over the last ten years, research in the field of dynamic programming has assumed many different forms. Sometimes, the emphasis has been upon questions of formulation in analytic terms and concepts, sometimes upon the problems of existence and uniqueness of solutions of the functional equations derived from the underlying processes, occasionally upon the actual analytic structure of the solutions of these equations, sometimes upon the computational aspects; and sometimes upon the applications-to control processes, to trajectories of various types, to operations research, to mathematical economics. Inevitably, the result of this quasi-ergodic behavior has been to ignore a number of significant problems, and to treat a number of others in cavalier fashion. In this exposition, we wish to focus attention upon a number of interesting, difficult, and significant questions in analysis which arise naturally out of the functional equation technique of dynamic programming. Our aim is to show that this theory constitutes a natural extension of classical investigations and that the corresponding problems are natural generalizations of problems of classical analysis."@en

genre

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  • "Bibliography"
  • "Bibliography"@en
  • "Electronic books"@en
  • "Electronic books"
  • "Mathematical formulae"@en

name

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  • "Dynamic programming, generalized states, and switching systems"@en
  • "Dynamic programming. [Supplement, by] Richard Bellman and Rebecca Karush"@en
  • "Dynamic programming : A bibliography of theory and application"
  • "Dynamic programming of continuous processes"@en
  • "Dynamic programming of continuous processes"
  • "Dynamic programming and mean square deviation"
  • "Dynamic programming and mean square deviation"@en
  • "Dinamičeskoe programmirovanie"
  • "Dynamic programming and classical analysis"@en
  • "Dynamic programming, invariant imbedding and quasilinearization : comparisons and interconnections"@en
  • "DYNAMIC PROGRAMMING AND MATHEMATICAL ECONOMICS"@en
  • "Dynamic programming and the computational solution of feedback design control problems"@en
  • "Dynamic Programming"@en
  • "A DYNAMIC PROGRAMMING SOLUTION TO A CASCADING PROBLEM ARISING IN HEAVY WATER PRODUCTION"@en
  • "Dynamic programming and its application to variational problems in mathematical economics"@en
  • "Dynamic programming : a bibliography of theory and application"@en
  • "Dynamic programming : a bibliography of theory and application"
  • "Dynamic Programming"
  • "Dynamic programming and the numerical solution of variational problems"@en
  • "Dynamic programming and the variation of green's functions"@en
  • "Dynamic programming approach to optimal inventory processes with delay in delivery"@en
  • "Dynamic programming : a reluctant theory"
  • "Dynamic programming, successive approximations and variational problems of combinatorial nature"@en
  • "Dynamic programming and modern control"
  • "Dynamic programming and ill-conditioned linear systems"@en
  • "Dynamic programming, learning, and adaptive processes"@en
  • "Dynamic programming: a bibliography of theory and application"@en
  • "Dynamic programming and mathematical economics"@en
  • "Dynamic programming and modern control theory"
  • "DYNAMIC PROGRAMMING"@en
  • "Dinamicheskoe programmirovanie"
  • "Dynamic programming and Markovian decision processes : with application to baseball"
  • "Dynamic programming and inverse optimal problems in mathematical economics"@en
  • "Dynamic programming, system identification, and suboptimization"@en
  • "Dynamic programming and a new formalism in the calculus of variations"@en
  • "Dynamic programming and a new formalism in the theory of integral equations"@en
  • "Dynamic programming and an inverse problem in neutron transport theory"@en
  • "Dynamic programming strategies in scan-rescan processes for tumor detection"
  • "Dynamic programming and the variational solution of the thomas-fermi equation"@en
  • "Dynamic programming and lagrange multipliers"@en
  • "Dynamic programming"@en
  • "Dynamic programming"
  • "Dynamic programming and stochastic control processes"@en
  • "Dynamic programming : (2. print.)"
  • "Dynamic programming, invariant imbedding and quasilinearization. comparisons and interconnections"@en
  • "Dynamic programming, nonlinear variational processes, and successive approximations"@en
  • "Dynamic programming and bicubic spline interpolation"@en
  • "Dynamic programming applied to control processes governed by general functional equations"@en
  • "Dynamic programming and multi-stage decision processes of stochastic type"@en
  • "Dynamic programming and linear prediction theory"@en
  • "Dynamic programming and artificial intelligence"
  • "Dynamic programming, sequential estimation and sequential detection processes"@en
  • "Dynamic programming : [a Rand Corporation research study]"@en
  • "Dynamic programming, intelligent machines, and self-organizing systems"@en

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