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], then it can be detected after *c*_{p}(*n*)=「2log_{「p/2」+1}(n+1)」-1 parallel evaluations of *f(x)*, where p is the number of processors.

Keywords

Adversarial Minimax Analysis, Design Parameters, Dynamic Programming, Function Evaluation, Optimal Algorithm, Parallel Algorithm, System Design, Statistical Experiments, Time Complexity, Unbounded Search, Unimodal Function

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B. Verkhovsky, "Parallel Minimax Searching Algorithm for Extremum of Unimodal Unbounded Function," *International Journal of Communications, Network and System Sciences*, Vol. 4 No. 9, 2011, pp. 549-561. doi: 10.4236/ijcns.2011.49066.

Conflicts of Interest

The authors declare no conflicts of interest.

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