One of the most successful and widely used updating formulas is known as BFGS for its four developers, Broyden, Fletcher, Goldfarb, and Shanno. It is a rank two update with inherent positive-definiteness (i.e., positive-definite positive-definite), and was derived by ``symmetrizing'' the Broyden rank one update. A sequence of matrices is generated from a positive-definite (which may be taken as the identity), by the following BFGS formula:

where