Open AccessA class of singular Ro-matrices and extensions to semidefinite linear complementarity problems
Author(s) -
K. C. Sivakumar
Publication year - 2013
Publication title -
yugoslav journal of operations research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.221
H-Index - 21
eISSN - 1820-743X
pISSN - 0354-0243
DOI - 10.2298/yjor130105027s
Subject(s) - mathematics , linear complementarity problem , complementarity (molecular biology) , complementarity theory , positive definite matrix , mixed complementarity problem , combinatorics , matrix (chemical analysis) , class (philosophy) , subspace topology , pure mathematics , transformation matrix , linear map , discrete mathematics , eigenvalues and eigenvectors , mathematical analysis , computer science , nonlinear system , physics , genetics , quantum mechanics , artificial intelligence , biology , materials science , kinematics , classical mechanics , composite material
For ARnxn and qRn, the linear complementarity problem LCP(A, q) is to determine if there is xRn such that x ≥ 0; y = Ax + q ≥ 0 and xT y = 0. Such an x is called a solution of LCP(A,q). A is called an Ro-matrix if LCP(A,0) has zero as the only solution. In this article, the class of R0-matrices is extended to include typically singular matrices, by requiring in addition that the solution x above belongs to a subspace of Rn. This idea is then extended to semidefinite linear complementarity problems, where a characterization is presented for the multplicative transformation