On superlinear convergence of quasi-Newton methods for nonsmooth equations |
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Authors: | Liqun Qi |
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Affiliation: | aSchool of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia |
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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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Keywords: | Nonsmooth equations Quasi-Newton methods The Broyden method Superlinear convergence |
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