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Zbl 1205.90002
Bellman, Richard
(Dreyfus, Stuart)
Dynamic programming. With a new introduction by Stuart Dreyfus. Reprint of the 1957 ed. (English)
[B] Princeton Landmarks in Mathematics. Princeton, NJ: Princeton University Press. xxx, 340~p. \sterling~27.95; \$~39.50 (2010). ISBN 978-0-691-14668-3/pbk

The purpose of this book is to provide an introduction to dynamic programming. In the first chapter a multi-stage decision process in both deterministic and stochastic types is considered. In the second chapter a stochastic multi-stage decision process in the guise of a gold-mining venture is discussed and the idea of decision regions is introduced. In the third chapter the formulation of the general decision process is derived and the author states the principle of optimality. In Chapter IV, a number of existence and uniqueness theorems are established for general equations of the preceding chapter. In Chapter V, the optimal inventory problem is discussed. Chapter VI and Chapter VII are devoted to bottleneck problems. In Chapter VIII a continuous version of the gold-mining process is considered. It is shown that a number of problems unsolved in their discrete versions can be solved completely in the continuous version. In this chapter the author combines the classical variational approach with the techniques employed in previous chapters. In Chapter IX the author shows that continuous variational problems may be viewed as dynamic programming of continuous and deterministic type. Chapter X is devoted to dynamic programming processes involving two decision-makers, essentially opposed to each other in their interests. Markovian decision processes are considered in the final chapter. A number of interesting results are given as exercises at the end of most chapters. Each chapter is completed with a bibliography. See also the review of the first edition (1957; Zbl 0077.13605),
[Svetlana A. Kravchenko (Minsk)]

MSC 2000:: *90-01 Textbooks (optimization)
90-02 Research monographs (optimization)
90C39 Dynamic programming
49L20 Dynamic programming method (infinite-dimensional problems)

Keywords: optimization; multi-stage decision process; deterministic process; stochastic process

Citations: Zbl 0077.13605; Zbl 1029.90076

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