Reference : Local convergence of quasi-Newton methods under metric regularity
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/10876
Local convergence of quasi-Newton methods under metric regularity
English
Aragón Artacho, Francisco Javier mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Belyakov, A. [> >]
Dontchev, A. L. [> >]
López, M. []
2014
Computational Optimization and Applications
58
1
225-247
Yes
International
[en] generalized equation ; quasi-Newton ; Broyden update
[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.
Luxembourg Centre for Systems Biomedicine (LCSB): Systems Biochemistry (Fleming Group)
http://hdl.handle.net/10993/10876
10.1007/s10589-013-9615-y
http://www.scopus.com/inward/record.url?eid=2-s2.0-84886218817&partnerID=40&md5=ae8acb340b1a045fa125a0003f191105

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