An analytic comparison of random searching and gradient searching for the extremum of a known objective function

The relative efficiencies of random searching and gradient searching for the extremum of a known function can be measured by a so-called search loss measure developed by Rastrigan [1]. It will be shown that a simple modification to the basic random searching strategy [1] can lead to a significant relative improvement in the efficiency, i.e., rate of convergence, of the random search.