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Generalizations in the linear search problem

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Abstract

A major part of the paper deals with the linear search problem in which the cost function is a strictly increasing convex functionf satisfyingf(0)=0. It is shown that a number of results previously established for the casef(t)=t α can be extended to the convex case; in particular a sufficient condition for the existence of a minimizing search strategy of a simple form is obtained for the convex case. Numerous results are obtained on the existence or otherwise of terminating and non-terminating optimal search strategies for cost functions already occurring in the literature.

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Authors and Affiliations

  1. Department of Mathematics, University of Southampton, SO9 5NH, Southampton, U.K.

    Vic Baston

  2. Department of Mathematics, University of Wisconsin, 53706, Madison, Wisconsin, U.S.A.

    Anatole Beck

Authors
  1. Vic Baston
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  2. Anatole Beck
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Correspondence to Vic Baston.

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Baston, V., Beck, A. Generalizations in the linear search problem. Israel J. Math. 90, 301–323 (1995). https://doi.org/10.1007/BF02783218

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  • DOI: https://doi.org/10.1007/BF02783218

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