  


An algorithmic characterization of Pmatricity II: adjustments, refinements, and validation
Ibtihel Ben Gharbia (ibtihel.bengharbiaifpen.fr) Abstract: The paper "An algorithmic characterization of Pmatricity" (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 Newtonmin algorithm for solving a linear complementarity problem of dimension n, which reads 0 ⩽ x ⊥ (M x + q) ⩾ 0, are uniquely determined by some index subsets of [[1, n]]. Even if this is satisfied for a subset of vectors q that is dense in 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 Pmatrix if and only if the Newtonmin algorithm does not cycle between two distinct points, whatever is q. The proof is not more complex, requiring only some adjustments, which are essential however. Keywords: linear complementarity problem, NMmatrix, Newtonmin algorithm, Pmatricity characterization, Pmatrix, semismooth Newton method. Category 1: Complementarity and Variational Inequalities Citation: SIAM Journal on Matrix Analysis and Applications (to appear) Download: [PDF] Entry Submitted: 09/29/2018 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  