Before revision:  In each iteration, PNKH-B generates a low-rank approximation of the (approximate) Hessian using Lanczos tridiagonalization and then solves a quadratic projection problem to update the iterate .
After revision:  In each iteration, PNKH-B generates a low-rank approximation of the (approximate) Hessian to determine the search direction and construct the metric used in a projected line search .