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Dettaglio pubblicazione

2017, JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, Pages 369-401 (volume: 172)

A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization (01a Articolo in rivista)

Cristofari Andrea, DE SANTIS Marianna, Lucidi Stefano, Rinaldi Francesco

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 (J Optim Theory Appl 85(2):265–289, 1995)with amodification of the non-monotone line search framework recently proposed in De Santis et al. (Comput Optim Appl 53(2):395–423, 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 showthat the algorithm converges at a superlinear rate. Promising experimental results demonstrate the effectiveness of the proposed method.
Gruppo di ricerca: Continuous Optimization
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