  In this paper, we describe a two-stage method for solving optimization
problems with bound constraints. It combines the active-set estimate described
in [Facchinei and Lucidi, 1995] with a modification of the non-monotone line
search framework recently proposed in [De Santis et al., 2012]. In the first
stage, the algorithm exploits a property of the active-set estimate that
ensures a significant reduction in the objective function when setting to the
bounds all those variables estimated active. In the second stage, a
truncated-Newton strategy is used in the subspace of the variables estimated
non-active. In order to properly combine the two phases, a proximity check is
included in the scheme. This new tool, together with the other theoretical
features of the two stages, enables us to prove global convergence.
Furthermore, under additional standard assumptions, we can show that the
algorithm converges at a superlinear rate. Promising experimental results
demonstrate the effectiveness of the proposed method.
