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A family of Newton methods for nonsmooth constrained systems with nonisolated solutions. (English) Zbl 1269.49046

Summary: 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 non-isolated solutions, and improve corresponding existing results.

MSC:

49M15 Newton-type methods
90C05 Linear programming
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References:

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