  This paper presents a finite difference quasi-Newton method for the
minimization of noisy functions. The method takes advantage of the scalability
and power of BFGS updating, and employs an adaptive procedure for choosing the
differencing interval $h$ based on the noise estimation techniques of Hamming
(2012) and Mor\'e and Wild (2011). This noise estimation procedure and the
selection of $h$ are inexpensive but not always accurate, and to prevent
failures the algorithm incorporates a recovery mechanism that takes appropriate
action in the case when the line search procedure is unable to produce an
acceptable point. A novel convergence analysis is presented that considers the
effect of a noisy line search procedure. Numerical experiments comparing the
method to a function interpolating trust region method are presented.
