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

Andrea Cristofari (), Marianna Santis (), Stefano Lucidi () and Francesco Rinaldi ()
Additional contact information
Andrea Cristofari: Sapienza University of Rome
Marianna Santis: Alpen-Adria-Universität Klagenfurt
Stefano Lucidi: Sapienza University of Rome
Francesco Rinaldi: University of Padova

Journal of Optimization Theory and Applications, 2017, vol. 172, issue 2, No 3, 369-401

Abstract: 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.

Keywords: Bound-constrained optimization; Large-scale optimization; Active-set methods; Non-monotone stabilization techniques; 90C30; 90C06; 49M15 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-016-1024-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:172:y:2017:i:2:d:10.1007_s10957-016-1024-9

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-016-1024-9

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().