A superlinearly convergent ODE-type trust region algorithm for nonsmooth nonlinear equations

This paper presents a new trust region algorithm for solving nonsmooth nonlinear equation problems which posses the smooth plus non-smooth decomposition. At each iteration, this method obtains a trial step by solving a system of linear equations, hence avoiding the need for solving a quadratic progr...

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Bibliographic Details
Published in:Journal of applied mathematics & computing Vol. 22; no. 3; pp. 371 - 380
Main Author: Yigui, Ou
Format: Journal Article
Language:English
Published: Dordrecht Springer Nature B.V 01.10.2006
Subjects:
Algorithms
Nonlinear equations
Studies
ISSN:1598-5865, 1865-2085
Online Access:Get full text
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Summary:This paper presents a new trust region algorithm for solving nonsmooth nonlinear equation problems which posses the smooth plus non-smooth decomposition. At each iteration, this method obtains a trial step by solving a system of linear equations, hence avoiding the need for solving a quadratic programming subproblem with a trust region bound. From a computational point of view, this approach may reduce computational effort and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and locally super-linearly convergent. Some numerical examples are reported.[PUBLICATION ABSTRACT]
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ISSN:1598-5865
1865-2085
DOI:10.1007/BF02832062