On superlinear convergence of quasi-Newton methods for nonsmooth equations

On superlinear convergence of quasi-Newton methods for nonsmooth equations

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Article ID: iaor19982993
Country: Netherlands
Volume: 20
Issue: 5
Start Page Number: 223
End Page Number: 228
Publication Date: Jun 1997
Journal: Operations Research Letters
Authors:
Keywords: Newton method, convergence
Abstract:

We show that strong differentiability at solutions is not necessary for superlinear convergence of quasi-Newton methods for solving nonsmooth equations. We improve the superlinear convergence result of Ip and Kyparisis for general quasi-Newton methods as well as the Broyden method. For a special example, the Newton method is divergent but the Broyden method is superlinearly convergent.

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