A new family of limited-memory variable metric or quasi-Newton methods for unconstrained minimization is given. The methods are based on a positive definite inverse Hessian approximation in the form of the sum of identity matrix and two low rank matrices, obtained by the standard scaled Broyden class update. To reduce the rank of matrices, various projections are used. Numerical experience is encouraging.
Technical report No. V 1036, Institute of Computer Science, Pod Vodarenskou Vezi 2, 18207 Praha 8. December 2008