{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:43:31Z","timestamp":1787330611273,"version":"build-2736575974"},"reference-count":32,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>The paper \u201cAn Algorithmic Characterization of P-Matricity\u201d [ SIAM J. Matrix Anal. Appl., 34 (2013), pp. 904--916], by the same authors as here, implicitly assumes that the iterates generated by the Newton-min algorithm for solving a linear complementarity problem of dimension $n$, which reads $0\\leq x\\perp(Mx+q)\\geq0$, are uniquely determined by some index subsets of $\\llbracket 1,n \\rrbracket$. Even if this is satisfied for a subset of vectors $q$ that is dense in $\\mathbb{R}^n$, this assumption is improper, in particular in the statements where the vector $q$ is not subject to restrictions. The goal of the present contribution is to show that, despite this blunder, the main result of that paper is preserved. This one claims that a nondegenerate matrix $M$ is a P-matrix if and only if the Newton-min algorithm does not cycle between two distinct points, whatever $q$ is. The proof is not more complex, requiring only some adjustments, which are essential, however.<\/jats:p>","DOI":"10.1137\/18m1168522","type":"journal-article","created":{"date-parts":[[2019,6,27]],"date-time":"2019-06-27T13:37:47Z","timestamp":1561642667000},"page":"800-813","source":"Crossref","is-referenced-by-count":9,"title":["An Algorithmic Characterization of P-matricity II: Adjustments, Refinements, and Validation"],"prefix":"10.1137","volume":"40","author":[{"given":"I. Ben","family":"Gharbia","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0375-4663","authenticated-orcid":true,"given":"J. Ch.","family":"Gilbert","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,6,27]]},"reference":[{"key":"atypb1","unstructured":"I. Ben Gharbia and J. Ch. Gilbert,\n                      Nonconvergence of the plain Newton-min algorithm for linear complementarity problems with a $P$-matrix-The full report\n                      , Research report 7160, INRIA, France, 2009."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-010-0439-6"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/120883025"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2013.04.021"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623498343131"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012997328609"},{"key":"atypb7","unstructured":"J. Bonnans, J. Ch. Gilbert, C. Lemar\u00e9chal, and C. Sagastiz\u00e1bal,\n                      Optimisation Num\u00e9rique-Aspects Th\u00e9oriques et Pratiques\n                      , Math. Appl. 27, Springer, Berlin, 1997."},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"J. Bonnans, J. Ch. Gilbert, C. Lemar\u00e9chal, and C. Sagastiz\u00e1bal,\n                      Numerical Optimization-Theoretical and Practical Aspects\n                      , 2nd ed., Universitext, Springer, Berlin, 2006,https:\/\/doi.org\/10.1007\/978-3-540-35447-5.","DOI":"10.1007\/978-3-540-35447-5"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-015-0965-3"},{"key":"atypb10","first-page":"263","volume":"7","author":"Chandrasekaran R.","year":"1970","journal-title":"Opsearch"},{"key":"atypb11","first-page":"425","volume":"23","author":"Chiche A.","year":"2016","journal-title":"J. Convex Anal."},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"R. Cottle, J.S. Pang, and R. Stone,\n                      The Linear Complementarity Problem\n                      , Classics Appl. Math. 60, SIAM, Philadelphia, 2009.","DOI":"10.1137\/1.9780898719000"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-014-9681-9"},{"key":"atypb14","first-page":"45","volume":"12","author":"Delbos F.","year":"2005","journal-title":"J. Convex Anal."},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"J.P. Dussault, M. Frappier, and J. Ch. Gilbert,\n                      A lower bound on the iterative complexity of the Harker and Pang globalization technique of the Newton-min algorithm for solving the linear complementarity problem\n                      , EURO J. Comput. Optim., to appear, 2019.","DOI":"10.1007\/s13675-019-00116-6"},{"key":"atypb16","unstructured":"M. Ferris and J.S. Pang,\n                      Complementarity and Variational Problems-State of the Art\n                      , in Proceedings of the International Conference on Complementarity Problems, Baltimore, MD, SIAM, Philadelphia, 1997."},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144595285963"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.21136\/CMJ.1962.100526"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/BF02592200"},{"key":"atypb20","unstructured":"P. Harker and J.S. Pang,\n                      A damped-Newton method for the linear complementarity problem\n                      , in Computational Solution of Nonlinear Systems of Equations, E. Allgower and K. Georg, eds., Lect. Appl. Math. 26, AMS, Providence, RI, 1990."},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623401383558"},{"key":"atypb22","unstructured":"P. Hungerl\u00e4nder, J. J\u00fadice, and F. 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