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Theory of Optimal Search

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Theory of Optimal Search, 9781877640001 (187764000X), MAS, 2007
This book deals with the problem of optimal allocation of effort to detect a  target. A Bayesian approach is taken in which it is assumed that there is a  prior distribution for the target's location which is known to the searcher as  well as a function which relates the conditional probability of detecting a  target given it is located at a point (or in a cell) to the effort applied there.  Problems involving computer search for the maximum of a function do not,  for the most part, conform to this framework and are not addressed.  The allocation problems considered are all one-sided in the sense that only  the searcher chooses how to allocate effort. For example, the target is  allowed to move but not to evade. Thus, pursuit and evasion problems are not  considered. 

The primary focus of the book is on problems in which the target is  stationary. For this case, we use a generalized Lagrange multiplier technique,  which allows inequality constraints and does not require differentiability  assumptions, to provide a unified method for finding optimal search   allocations. This method is also extended to find optimal plans in some cases   involving false and moving targets. For the case of Markovian target motion,  results are, for the most part, presented without proof, and the reader is  referred to the appropriate papers for proofs. 

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