Generalizations in the linear search problem

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)=tα 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.