zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Dynamic programming. With a new introduction by Stuart Dreyfus. Reprint of the 1957 ed. (English) Zbl 1205.90002
Princeton Landmarks in Mathematics. Princeton, NJ: Princeton University Press (ISBN 978-0-691-14668-3/pbk). xxx, 340 p. £ 27.95; $ 39.50 (2010).

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),

90-01Textbooks (optimization)
90-02Research monographs (optimization)
90C39Dynamic programming
49L20Dynamic programming method (infinite-dimensional problems)