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An algorithmic characterization of P-matricity II: adjustments, refinements, and validation

Published: 2018/09/29, Updated: 2019/04/12

Complementarity and Variational Inequalities linear complementarity problems, newton-min algorithm, nm-matrix, p-matricity characterization, p*-matrix, semismooth newton method

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

An algorithmic characterization of P-matricity

Published: 2012/06/29, Updated: 2013/02/15

Ibtihel Ben Gharbia

Jean Charles Gilbert

Complementarity and Variational Inequalities linear complementarity problems, newton-min algorithm, nm-matrix, p*-matrix, semismooth newton method

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