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Newton methods for solving nonsmooth equations via a new subdifferential

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  • Yan Gao

Abstract

A new subdifferential for a locally Lipschitzian function is proposed. Based on this subdifferential, Newton methods and inexact-Newton methods for solving the system of nonsmooth equations and for solving the system of equations of smooth compositions of nonsmooth functions, are developed. The Q-superlinear convergence of Newton methods and the Q-linear convergence of inexact-Newton methods are shown. The present Newton methods and inexact-Newton methods could be viewed as the extensions of previous ones with same convergent results. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • Yan Gao, 2001. "Newton methods for solving nonsmooth equations via a new subdifferential," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(2), pages 239-257, December.
    • Handle: RePEc:spr:mathme:v:54:y:2001:i:2:p:239-257
    DOI: 10.1007/s001860100150
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    Cited by:

    1. Pickl, Stefan, 2004. "Solving the semismooth equivalence problem," European Journal of Operational Research, Elsevier, vol. 157(1), pages 68-73, August.
    2. Shuhuang Xiang & Xiaojun Chen, 2011. "Computation of generalized differentials in nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 50(2), pages 403-423, October.

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