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A Newton-type method for positive-semidefinite linear complementarity problems

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Abstract

The paper presents a damped and perturbed Newton-type method for solving linear complementarity problems with positive-semidefinite matricesM. In particular, the following properties hold: all occurring subproblems are linear equations; each subproblem is uniquely solvable without any assumption; every accumulation point generated by the method solves the linear complementarity problem. The additional property ofM to be an R0-matrix is sufficient, but not necessary, for the boundedness of the iterates. Provided thatM is positive definite on a certain subspace, the method converges Q-quadratically.

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Authors and Affiliations

  1. Department of Mathematics, Dresden University of Technology, Dresden, Germany

    A. Fischer (Research Assistant)

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  1. A. Fischer
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Communicated by G. Di Pillo

The author would like to thank the anonymous referees and Dr. K. Schönefeld for their valuable comments and suggestions. He is also grateful to Prof. Dr. J. W. Schmidt for his continuous interest in this study.

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Fischer, A. A Newton-type method for positive-semidefinite linear complementarity problems. J Optim Theory Appl 86, 585–608 (1995). https://doi.org/10.1007/BF02192160

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