Before revision:  We provide a convergence analysis of SP-BFGS, and present numerical results illustrating the performance of SP-BFGS  in the presence of noisy gradients .
After revision:  We provide a convergence analysis of SP-BFGS, including convergence when minimizing strongly convex functions in the presence of uniformly bounded noise. Finally, we present extensive numerical experiments using over 30 problems from the CUTEst test problem set that demonstrate the superior performance of SP-BFGS in the presence of noisy gradients .