The paper “An algorithmic characterization of P-matricity” (SIAM Journal on Matrix Analysis and Applications, 34:3 (2013) 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 ⩽ x ⊥ (M x + q) ⩾ 0, are … Read more
The plain Newton-min algorithm for solving the linear complementarity problem (LCP) 0 ≤ x ⊥ (Mx+q) ≥ 0 can be viewed as an instance of the plain semismooth Newton method on the equational version min(x,Mx+q) = 0 of the problem. This algorithm converges for any q when M is an M-matrix, but not when it … Read more
It is shown that a matrix $M$ is a P-matrix if and only if, whatever is the vector $q$, the Newton-min algorithm does not cycle between two points when it is used to solve the linear complementarity problem $0\leq x\perp (Mx+q)\geq0$. CitationInria research report RR-8004ArticleDownload View PDF