Aragón Artacho, Francisco Javier, Belyakov, Anton O., Dontchev, Asen L., López Cerdá, Marco A.
Local convergence of quasi-Newton methods under metric regularity
Computational Optimization and Applications. 2013, October. doi:10.1007/s10589-013-9615-y
URI: http://hdl.handle.net/10045/35901
DOI: 10.1007/s10589-013-9615-y
ISSN: 0926-6003 (Print)
Abstract: 
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.
Keywords:Generalized equation, Quasi-Newton method, Broyden update, Strong metric subregularity, Metric regularity, Strong metric regularity, q-Superlinear convergence
Springer Science+Business Media New York
info:eu-repo/semantics/article