Golden Block Search for the Maximum of Unimodal Functions

Abstract

In a previous paper [Avriel, M., D. J. Wilde. 1966. Optimal search for a maximum with sequences of simultaneous function evaluations. Management Sci. 12 722.], the authors presented the minimax block search strategy for locating the maximum of unimodal functions of one variable by a sequence of simultaneous function evaluations. In the present work the nearly optimal minimax golden block search method is developed which has the advantage that the number of function evaluations need not be specified in advance. For one experiment per block it reduces to the well known golden section method. It is shown that this method is an excellent approximation of the block search strategy and that for a certain marginal resolution the two methods become identical.