A family of Newton methods for nonsmooth constrained systems with nonisolated solutions |
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Authors: | Francisco Facchinei Andreas Fischer Markus Herrich |
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Affiliation: | 1. Department of Computer, Control, and Management Engineering Antonio Ruberti, University of Rome La Sapienza, Via Ariosto 25, 00185, Roma, Italy 2. Department of Mathematics, Institute of Numerical Mathematics, Technische Universit?t Dresden, 01062, Dresden, Germany
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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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