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See detailLocal convergence of quasi-Newton methods under metric regularity
Aragón Artacho, Francisco Javier UL; Belyakov, A.; Dontchev, A. L. et al

in Computational Optimization and Applications (2014), 58(1), 225-247

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 ... [more ▼]

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. [less ▲]

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