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A two-stage active-set algorithm for bound-constrained optimization. (English) Zbl 1398.90170
Summary: In this paper, we describe a two-stage method for solving optimization problems with bound constraints. It combines the active-set estimate described in [F. Facchinei and S. Lucidi, J. Optim. Theory Appl. 85, No. 2, 265–289 (1995; Zbl 0830.90125)] with a modification of the non-monotone line search framework recently proposed in [M. De Santis et al., Comput. Optim. Appl. 53, No. 2, 395–423 (2012; Zbl 1284.90075)]. 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.

90C30 Nonlinear programming
90C06 Large-scale problems in mathematical programming
49M15 Newton-type methods
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