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An LP-Newton method: nonsmooth equations, KKT systems, and nonisolated solutions

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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, thus filling an important gap in the existing theory. The new algorithm improves on known methods and, when particularized to KKT systems derived from optimality conditions for constrained optimization or variational inequalities, it has theoretical advantages even over methods specifically designed to solve such systems.

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Acknowledgments

We wish to thank the anonymous referees for their valuable comments.

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Authors and Affiliations

  1. Department of Computer, Control, and Management Engineering Antonio Ruberti, University of Rome La Sapienza, Via Ariosto 25, 00185 , Roma, Italy

    Francisco Facchinei

  2. Department of Mathematics, Institute of Numerical Mathematics, Technische Universität Dresden, 01062 , Dresden, Germany

    Andreas Fischer & Markus Herrich

Authors
  1. Francisco Facchinei
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  2. Andreas Fischer
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  3. Markus Herrich
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Corresponding author

Correspondence to Andreas Fischer.

Additional information

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.

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Facchinei, F., Fischer, A. & Herrich, M. An LP-Newton method: nonsmooth equations, KKT systems, and nonisolated solutions. Math. Program. 146, 1–36 (2014). https://doi.org/10.1007/s10107-013-0676-6

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  • DOI: https://doi.org/10.1007/s10107-013-0676-6

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