  In this paper, we study greedy variants of quasi-Newton methods. They are
based on the updating formulas from a certain subclass of the Broyden family.
In particular, this subclass includes the well-known DFP, BFGS and SR1 updates.
However, in contrast to the classical quasi-Newton methods, which use the
difference of successive iterates for updating the Hessian approximations, our
methods apply basis vectors, greedily selected so as to maximize a certain
measure of progress. For greedy quasi-Newton methods, we establish an explicit
non-asymptotic bound on their rate of local superlinear convergence, which
contains a contraction factor, depending on the square of the iteration
counter. We also show that these methods produce Hessian approximations whose
deviation from the exact Hessians linearly convergences to zero.
