An algorithm for the rapid location of an extreme of a function subject only to geometric restrictions

The requirements of symmetry and convexity in the application of algorithms for the minimization or maximization of a function are discussed. It is argued that if a function of a single variable is convex and symmetric in a neighborhood of an extremum, the extremum may be approximated to the precision that increases by at least a power of two per functional evaluation. The procedure may be used to drive a complex optimization procedure in the multivariate area estimation problem encountered in remote sensing.