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A modified damped Newton method for linear complementarity problems

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Abstract

We present a modified damped Newton method for solving large sparse linear complementarity problems, which adopts a new strategy for determining the stepsize at each Newton iteration. The global convergence of the new method is proved when the system matrix is a nondegenerate matrix. We then apply the matrix splitting technique to this new method, deriving an inexact splitting method for the linear complementarity problems. The global convergence of the resulting inexact splitting method is proved, too. Numerical results show that the new methods are feasible and effective for solving the large sparse linear complementarity problems.

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Authors and Affiliations

  1. State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100080, People's Republic of China

    Zhong-Zhi Bai & Jun-Liang Dong

Authors
  1. Zhong-Zhi Bai
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  2. Jun-Liang Dong
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Correspondence to Zhong-Zhi Bai.

Additional information

The research of this author is supported by The National Basic Research Program (No. 2005CB321702), The China NNSF National Outstanding Young Scientist Foundation (No. 10525102) and The National Natural Science Foundation (No. 10471146), P.R. China.

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Bai, ZZ., Dong, JL. A modified damped Newton method for linear complementarity problems. Numer Algor 42, 207–228 (2006). https://doi.org/10.1007/s11075-006-9028-4

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