Aragon Artacho, F. J., Belyakov, A., Dontchev, A., & Lopez, M. (2013). Local convergence of quasi-Newton methods under metric regularity. Computational Optimization and Applications, 58(1), 225–247. https://doi.org/10.1007/s10589-013-9615-y
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.
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Research Areas:
Mathematical Methods in Economics: 20% Mathematical and Algorithmic Foundations: 80%
