Time Delay in Minimax Optimization of Unimodal Functions of One Variable

A minimax search plan is developed for locating the maximum of a one dimensional unimodal function when a time delay occurs between the placement of an experiment and the result. The optimal search plans, among all the plans which place only one experiment at each unit of time, are determined for time delays of one and two periods. These plans are optimal in the sense that for a required final interval of uncertainty, they have the largest possible starting interval. Discrete variable (lattice) versions of these plans are also given, as well as plans for when the number of experiments is unknown initially. When more than one experiment can be made at each unit of time, a variant of block search is more efficient.