Before revision:  These developments allow us to develop an algorithm we refer to as secant penalized BFGS (SP-BFGS) that allows one to relax the secant condition based on the amount of noise in the gradient measurements.
After revision:  These developments allow us to develop a method we refer to as secant penalized BFGS (SP-BFGS) that allows one to relax the secant condition based on the amount of noise in the gradient measurements.