Local convergence of quasi-Newton methods under metric regularity

F. Aragón Artacho, Anton Belyakov, A. Dontchev () and M. López

Computational Optimization and Applications, 2014, vol. 58, issue 1, 225-247

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. Copyright Springer Science+Business Media New York 2014

Keywords: Generalized equation; Quasi-Newton method; Broyden update; Strong metric subregularity; Metric regularity; Strong metric regularity; q-Superlinear convergence (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10589-013-9615-y

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