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Title: Global Complexity Bound Analysis of the Levenberg–Marquardt Method for Nonsmooth Equations and Its Application to the Nonlinear Complementarity Problem
Authors: Ueda, Kenji
Yamashita, Nobuo  kyouindb  KAKEN_id
Author's alias: 上田, 健詞
Keywords: Levenberg–Marquardt methods
Global complexity bound
Nonlinear complementarity problems
Issue Date: Feb-2012
Publisher: Springer Science+Business Media, LLC
Journal title: Journal of Optimization Theory and Applications
Volume: 152
Issue: 2
Start page: 450
End page: 467
Abstract: We investigate a global complexity bound of the Levenberg–Marquardt Method (LMM) for nonsmooth equations. The global complexity bound is an upper bound to the number of iterations required to get an approximate solution that satisfies a certain condition. We give sufficient conditions under which the bound of the LMM for nonsmooth equations is the same as smooth cases. We also show that it can be reduced under some regularity assumption. Furthermore, by applying these results to nonsmooth equations equivalent to the nonlinear complementarity problem (NCP), we get global complexity bounds for the NCP. In particular, we give a reasonable bound when the mapping involved in the NCP is a uniformly P-function.
Rights: The final publication is available at
This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。
DOI(Published Version): 10.1007/s10957-011-9907-2
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