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dc.contributor.authorGilbert, J. Charles
dc.contributor.authorBen Gharbia, Ibtihel
dc.date.accessioned2011-04-26T15:01:38Z
dc.date.available2011-04-26T15:01:38Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6052
dc.language.isoenen
dc.subjectLinear complementarity problemen
dc.subjectNewton’s methoden
dc.subjectNonconvergenceen
dc.subjectNonsmooth functionen
dc.subjectM-matrixen
dc.subjectP-matrixen
dc.subject.ddc519en
dc.titleNonconvergence of the plain Newton-min algorithm for linear complementarity problems with a P-matrixen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThe plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) 0 £ x^(Mx+q) ³ 00x(Mx+q)0 can be viewed as a semismooth 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 paper that this result no longer holds when M is a P-matrix of order ≥ 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.en
dc.relation.isversionofjnlnameMathematical Programming
dc.relation.isversionofjnlvol134
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpages349-364
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s10107-010-0439-6en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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