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An LP-Newton Method: Nonsmooth Equations, KKT Systems, and 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 define a new Newton-type method for the solution of constrained systems of equations and analyze in detail its properties. Under suitable conditions, that do not include differentiability or local uniqueness of solutions, the method converges locally quadratically to a solution of the system of equations, thus filling an important gap in the existing theory. The new algorithm improves on known methods and, when particularized to KKT systems deriving from optimality conditions for constrained optimization or variational inequalities, it has theoretical advantages even over methods specifically designed to solve such systems.

Keywords: quadratic convergence, Newton method, nonsmooth system, nonisolated solution, KKT system

Category 1: Complementarity and Variational Inequalities

Category 2: Nonlinear Optimization

Citation: Mathematical Programming, DOI: 10.1007/s10107-013-0676-6, to appear

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Entry Submitted: 09/22/2011
Entry Accepted: 09/22/2011
Entry Last Modified: 03/14/2013

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