Parallel Minimax Searching Algorithm for Extremum of Unimodal Unbounded Function

In this paper we consider a parallel algorithm that detects the maximizer of unimodal function ( ) f x computable at every point on unbounded interval (0, )  . The algorithm consists of two modes: scanning and detecting. Search diagrams are introduced as a way to describe parallel searching algorithms on unbounded intervals. Dynamic programming equations, combined with a series of liner programming problems, describe relations between results for every pair of successive evaluations of function f in parallel. Properties of optimal search strategies are derived from these equations. The worst-case complexity analysis shows that, if the maximizer is located on a priori unknown interval ( n 1, ] n  , then it can be detected after parallel evaluations of /2 1( p      ( ) 2log 1) 1 p c n n        ( ) f x , where p is the number of processors.