On the Use of Restricted Pseudo-inverses for the Unified Derivation of Quasi-Newton Updates

A new approach for deriving minimum norm quasi-Newton updatesis given. We use restricted pseudo-inverses of a single linearoperator to derive all known useful minimum norm updates, includingthose preserving sparsity and symmetry. This approach is direct,and unifies the theory of minimum norm quasi-Newton updates.We also prove a generalization of a theorem of Dennis &Schnabel using this approach.