Abstract
We propose a new family of Newton-type methods for the solution of constrained systems of equations. Under suitable conditions, that do not include differentiability or local uniqueness of solutions, local, quadratic convergence to a solution of the system of equations can be established. We show that as particular instances of the method we obtain inexact versions of both a recently introduced LP-based Newton method and of a Levenberg-Marquardt algorithm for the solution of systems with nonisolated solutions, and improve on corresponding existing results.
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Acknowledgments
Part of this research was done while the second author was visiting the Department of Computer, Control, and Management Engineering Antonio Ruberti at the University of Rome La Sapienza. The financial support by the University of Rome La Sapienza is kindly acknowledged. The authors would like thank an anonymous referee for carefully reading the paper and helpful comments.
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Dedicated to Professor Hans-Jakob Lüthi on the occasion of his 65th birthday, in honor of his inspiring work in Operations Research.
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Facchinei, F., Fischer, A. & Herrich, M. A family of Newton methods for nonsmooth constrained systems with nonisolated solutions. Math Meth Oper Res 77, 433–443 (2013). https://doi.org/10.1007/s00186-012-0419-0
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DOI: https://doi.org/10.1007/s00186-012-0419-0