Geodesic
A Class of Singular $R_0$-Matrices and Extensions to Semidefinite Linear Complementarity Problems
Yugoslav journal of operations research, Tome 23 (2013) no. 2, p. 163

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

For $A \in \R^{n \times n}$ and $q \in \R^n$, the linear complementarity problem $LCP(A, q)$ is to determine if there is $x \in \R^n$ such that $x \geq 0,$ $y = Ax+q \geq 0$ and $x^T y = 0$. Such an $x$ is called a solution of $LCP(A, q)$. $A$ is called an $R_0$-matrix if $LCP(A, 0)$ has zero as the only solution. In this article, the class of $R_0$-matrices is extended to include typically singular matrices, by requiring in addition that the solution $x$ above belongs to a subspace of $\R^n$. This idea is then extended to semidefinite linear complementarity problems, where a characterization is presented for the multiplicative transformation.
Classification : 90C33, 15A09
Keywords: $R_0$-matrix, semidefinite linear complementarity problems, Moore-Penrose inverse, group inverse. 
@article{YJOR_2013_23_2_a1,
     author = {Koratti Chengalrayan Sivakumar},
     title = {A {Class} of {Singular} $R_0${-Matrices} and {Extensions} to {Semidefinite} {Linear} {Complementarity} {Problems}},
     journal = {Yugoslav journal of operations research},
     pages = {163 },
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/YJOR_2013_23_2_a1/}
}
TY  - JOUR
AU  - Koratti Chengalrayan Sivakumar
TI  - A Class of Singular $R_0$-Matrices and Extensions to Semidefinite Linear Complementarity Problems
JO  - Yugoslav journal of operations research
PY  - 2013
SP  - 163 
VL  - 23
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/YJOR_2013_23_2_a1/
LA  - en
ID  - YJOR_2013_23_2_a1
ER  - 
%0 Journal Article
%A Koratti Chengalrayan Sivakumar
%T A Class of Singular $R_0$-Matrices and Extensions to Semidefinite Linear Complementarity Problems
%J Yugoslav journal of operations research
%D 2013
%P 163 
%V 23
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/YJOR_2013_23_2_a1/
%G en
%F YJOR_2013_23_2_a1
Koratti Chengalrayan Sivakumar. A Class of Singular $R_0$-Matrices and Extensions to Semidefinite Linear Complementarity Problems. Yugoslav journal of operations research, Tome 23 (2013) no. 2, p. 163 . http://geodesic.mathdoc.fr/item/YJOR_2013_23_2_a1/