A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization

In this paper, we describe a two-stage method for solving optimization problems with bound constraints. It combines the active-set estimate described in [1] with a modification of the nonmonotone line search framework recently proposed in [2]. In the first stage, the algorithm exploits a property of the active-set estimate that ensures a significant reduction of 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.