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Globalizing a nonsmooth Newton method via nonmonotone path search

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  • Stephan Bütikofer

Abstract

We give a framework for the globalization of a nonsmooth Newton method. In part one we start with recalling B. Kummer’s approach to convergence analysis of a nonsmooth Newton method and state his results for local convergence. In part two we give a globalized version of this method. Our approach uses a path search idea to control the descent. After elaborating the single steps, we analyze and prove the global convergence resp. the local superlinear or quadratic convergence of the algorithm. In the third part we illustrate the method for nonlinear complementarity problems. Copyright Springer-Verlag 2008

Suggested Citation

  • Stephan Bütikofer, 2008. "Globalizing a nonsmooth Newton method via nonmonotone path search," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(2), pages 235-256, October.
    • Handle: RePEc:spr:mathme:v:68:y:2008:i:2:p:235-256
    DOI: 10.1007/s00186-008-0219-8
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    References listed on IDEAS

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    1. Shih-Ping Han & Jong-Shi Pang & Narayan Rangaraj, 1992. "Globally Convergent Newton Methods for Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 586-607, August.
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