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 a modification 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 show that the algorithm converges at a superlinear rate. Promising experimental results demonstrate the effectiveness of the proposed method.

Cristofari, A., DE SANTIS, M., Lucidi, S., Rinaldi, F. (2017). A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 172, 369-401 [10.1007/s10957-016-1024-9].

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

Cristofari, Andrea;
2017-01-01

Abstract

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 a modification 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 show that the algorithm converges at a superlinear rate. Promising experimental results demonstrate the effectiveness of the proposed method.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/09
English
Bound-constrained optimization
Large-scale optimization
Active-set methods
Non-monotone stabilization techniques
https://link.springer.com/article/10.1007/s10957-016-1024-9
Cristofari, A., DE SANTIS, M., Lucidi, S., Rinaldi, F. (2017). A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 172, 369-401 [10.1007/s10957-016-1024-9].
Cristofari, A; DE SANTIS, M; Lucidi, S; Rinaldi, F
Articolo su rivista
File in questo prodotto:
File Dimensione Formato  
(Cristofari et al., 2017) A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization.pdf

solo utenti autorizzati

Tipologia: Versione Editoriale (PDF)
Licenza: Copyright dell'editore
Dimensione 703.26 kB
Formato Adobe PDF
703.26 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/312069
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 18
  • ???jsp.display-item.citation.isi??? 17
social impact