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A Family of Newton Methods for Nonsmooth Constrained Systems with Nonisolated Solutions

Francisco Facchinei (facchinei***at***dis.uniroma1.it)
Andreas Fischer (Andreas.Fischer***at***tu-dresden.de)
Markus Herrich (Markus.Herrich***at***tu-dresden.de)

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.

Keywords: Quadratic convergence, inexact Newton method, nonsmooth system, nonisolated solution, Levenberg-Marquardt method

Category 1: Complementarity and Variational Inequalities

Category 2: Nonlinear Optimization

Citation: Mathematical Methods of Operations Research, to appear

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Entry Submitted: 12/06/2011
Entry Accepted: 12/06/2011
Entry Last Modified: 11/23/2012

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