Before revision:  We show that by treating the secant condition using a penalty method approach  , one can smoothly interpolate between updating the inverse Hessian approximation with the original BFGS update formula and not updating the inverse Hessian approximation.
After revision:  We show that by treating the secant condition using a penalty method approach motivated by regularized least squares estimation , one can smoothly interpolate between updating the inverse Hessian approximation with the original BFGS update formula and not updating the inverse Hessian approximation.