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Nonconvergence of the plain Newton-min algorithm for linear complementarity problems with a P-matrix.

Abstract : The plain Newton-min algorithm for solving the linear complementarity problem (LCP for short) 0≤ x \perp Mx+q ≥0 can be viewed as a nonsmooth Newton algorithm without globalization technique to solve the system of piecewise linear equations min(x,Mx+q)=0 , which is equivalent to the LCP. When M is an M-matrix of order n, the algorithm is known to converge in at most n iterations. We show in this note that this result no longer holds when M is a P-matrix of order n ≥3, since then the algorithm may cycle. P-matrices are interesting since they are those ensuring the existence and uniqueness of the solution to the LCP for an arbitrary q. Incidentally, convergence occurs for a P-matrix of order 1 or 2.
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https://hal.inria.fr/inria-00442293
Contributor : Ibtihel Ben Gharbia <>
Submitted on : Saturday, December 19, 2009 - 12:42:22 PM
Last modification on : Friday, May 25, 2018 - 12:02:03 PM
Long-term archiving on: : Thursday, June 17, 2010 - 11:56:57 PM

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  • HAL Id : inria-00442293, version 1

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Ibtihel Ben Gharbia, Jean Charles Gilbert. Nonconvergence of the plain Newton-min algorithm for linear complementarity problems with a P-matrix.. [Research Report] RR-7160, 2009. ⟨inria-00442293v1⟩

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