Global convergence property of modified Levenberg-Marquardt methods for nonsmooth equations

Shou-qiang Du; Yan Gao

Applications of Mathematics (2011)

  • Volume: 56, Issue: 5, page 481-498
  • ISSN: 0862-7940

Abstract

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In this paper, we discuss the globalization of some kind of modified Levenberg-Marquardt methods for nonsmooth equations and their applications to nonlinear complementarity problems. In these modified Levenberg-Marquardt methods, only an approximate solution of a linear system at each iteration is required. Under some mild assumptions, the global convergence is shown. Finally, numerical results show that the present methods are promising.

How to cite

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Du, Shou-qiang, and Gao, Yan. "Global convergence property of modified Levenberg-Marquardt methods for nonsmooth equations." Applications of Mathematics 56.5 (2011): 481-498. <http://eudml.org/doc/197232>.

@article{Du2011,
abstract = {In this paper, we discuss the globalization of some kind of modified Levenberg-Marquardt methods for nonsmooth equations and their applications to nonlinear complementarity problems. In these modified Levenberg-Marquardt methods, only an approximate solution of a linear system at each iteration is required. Under some mild assumptions, the global convergence is shown. Finally, numerical results show that the present methods are promising.},
author = {Du, Shou-qiang, Gao, Yan},
journal = {Applications of Mathematics},
keywords = {nonsmooth equations; modified Levenberg-Marquardt method; global convergence; nonlinear complementarity problem; numerical results; nonsmooth equation; modified Levenberg-Marquardt method; global convergence; nonlinear complementarity problem; numerical results},
language = {eng},
number = {5},
pages = {481-498},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Global convergence property of modified Levenberg-Marquardt methods for nonsmooth equations},
url = {http://eudml.org/doc/197232},
volume = {56},
year = {2011},
}

TY - JOUR
AU - Du, Shou-qiang
AU - Gao, Yan
TI - Global convergence property of modified Levenberg-Marquardt methods for nonsmooth equations
JO - Applications of Mathematics
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 5
SP - 481
EP - 498
AB - In this paper, we discuss the globalization of some kind of modified Levenberg-Marquardt methods for nonsmooth equations and their applications to nonlinear complementarity problems. In these modified Levenberg-Marquardt methods, only an approximate solution of a linear system at each iteration is required. Under some mild assumptions, the global convergence is shown. Finally, numerical results show that the present methods are promising.
LA - eng
KW - nonsmooth equations; modified Levenberg-Marquardt method; global convergence; nonlinear complementarity problem; numerical results; nonsmooth equation; modified Levenberg-Marquardt method; global convergence; nonlinear complementarity problem; numerical results
UR - http://eudml.org/doc/197232
ER -

References

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