Reference : Local convergence of quasi-Newton methods under metric regularity
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Local convergence of quasi-Newton methods under metric regularity
Aragón Artacho, Francisco Javier mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Belyakov, A. [> >]
Dontchev, A. L. [> >]
López, M. []
Computational Optimization and Applications
[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)

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