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

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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. 
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/
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