An efficient gradient flow method for unconstrained optimization
Walter Murray, William Behrman · 1998
This dissertation presents a method for unconstrained optimization based upon approximating the gradient flow of the objective function. Under mild assumptions the method is shown to converge to a critical point from any initial point and to converge quadratically in the neighborhood of a solution. Two implementations of the method are presented, one using explicit Hessians and $O(n\sp2)$ storage, the other using Hessian-vector products and O(n) storage. These implementations were written in ANSI-standard Fortran 77 for others to use. They have been extensively tested and have proven to be very reliable and efficient in comparison to leading alternative routines.