Dynamic ProgrammingAn introduction to the mathematical theory of multistage decision processes, this text takes a "functional equation" approach to the discovery of optimum policies. Written by a leading developer of such policies, it presents a series of methods, uniqueness and existence theorems, and examples for solving the relevant equations. 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, strategies behind multistage games, and Markovian decision processes. Each chapter concludes with a problem set that Eric V. Denardo of Yale University, in his informative new introduction, calls "a rich lode of applications and research topics." 1957 edition. 37 figures. |
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allocation analysis analytic approximation in policy assume assumption b₁ Bellman C₁ C₂ calculus of variations Chapter choice computational concave function Consider the problem constraints convergence convex convex function cost decision processes defined derive discussion dx/dt Dynamic Programming existence and uniqueness expected value f₁ finite fN+1 formulation function f functional equation Hence inequality initial interval K₁ l₁ Lemma linear machine mathematical Max F Max g Max q method minimize minimum multi-stage N-stage process nonlinear obtain optimal policy p₁ partial differential equation pi qj policy space probability problem of determining problem of maximizing proof quantity RAND Corporation recurrence relation region result satisfies Show solution stage Stieltjes integrals stochastic stochastic processes T₁ techniques theory tion variables variational problem vector w₁ x₁ y₁ yields