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A verification method for solutions of nonsmooth equations

Eine Methode zur Verifizierung von Lösungen nicht-differenzierbarer Gleichungen

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Abstract

This paper proposes a verification method for the existence of solutions of nonsmooth equations. We generalize the Krawczyk operator to nonsmooth equations by using the mean-value theorem for nonsmooth functions. We establish a semi-local convergence theorem for the generalized Newton method for nonsmooth equations. The proposed method is a combination of the generalized Krawczyk operator and the semi-local convergence theorem.

Zusammenfassung

Dieser Artikel schlägt eine Methode zur Verifizierung der Existenz von Lösungen nicht-differenzierbarer Gleichungen vor. Wir verallgemeinern den Krawczyk-Operator auf nicht-differenzierbare Gleichungen indem wir den Mittelwertsatz für nicht-differenzierbare Funktionen benutzen. Wir entwickeln einen semilokalen Konvergenzsatz für das verallgemeinerte Newton-Verfahren, angewendet auf nicht-differenzierbare Gleichungen. Die vorgeschlagene Methode ist eine Kombination aus dem verallgemeinerten Krawczyk-Operator und dem semi-lokalen Konvergenzsatz.

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Authors and Affiliations

  1. School of Mathematics, University of New South Wales, 2052, Sydney, NSW, Australia

    Xiaojun Chen

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  1. Xiaojun Chen
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This work is supported by the Australian Research Council.

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Chen, X. A verification method for solutions of nonsmooth equations. Computing 58, 281–294 (1997). https://doi.org/10.1007/BF02684394

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  • DOI: https://doi.org/10.1007/BF02684394

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