Article (Scientific journals)
Local convergence of quasi-Newton methods under metric regularity
Aragón Artacho, Francisco Javier; Belyakov, A.; Dontchev, A. L. et al.
2014In Computational Optimization and Applications, 58 (1), p. 225-247
Peer reviewed
 

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Keywords :
generalized equation; quasi-Newton; Broyden update
Abstract :
[en] We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity and strong metric regularity. In particular, we show that the Broyden update applied to a generalized equation in Hilbert spaces satisfies the Dennis–Moré condition for q-superlinear convergence. Simple numerical examples illustrate the results.
Research center :
Luxembourg Centre for Systems Biomedicine (LCSB): Systems Biochemistry (Fleming Group)
Disciplines :
Mathematics
Author, co-author :
Aragón Artacho, Francisco Javier ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Belyakov, A.
Dontchev, A. L.
López, M.
Language :
English
Title :
Local convergence of quasi-Newton methods under metric regularity
Publication date :
2014
Journal title :
Computational Optimization and Applications
Volume :
58
Issue :
1
Pages :
225-247
Peer reviewed :
Peer reviewed
Available on ORBilu :
since 15 November 2013

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