  The purpose of this paper is to present an inexact version of the scaled
gradient projection method on a convex set, which is inexact in two sense.
First, an inexact projection on the feasible set is computed, allowing for an
appropriate relative error tolerance. Second, an inexact non-monotone line
search scheme is employed to compute a step size which defines the next
iteration. It is shown that the proposed method has similar asymptotic
convergence properties and iteration-complexity bounds as the usual scaled
gradient projection method employing monotone line searches.
