Global error bound estimates algorithm for an R0-type generalized LCP over polyhedral cone and its applications

For the generalized linear complementarity problem over a polyhedral cone (GLCP), by making a characterization of $R_0$-matrix, we derive a necessary and sufficient condition for the boundedness of the level set of the natural residual function of the GLCP, and based on this, we establish a global error bound for the $R_0-$type GLCP. Compared with the existing results, the requirements imposed on the GLCP such as the non-degenerateness of the solution and the full-column rank of the underlying matrix are removed. As an application of the obtained results, we show the global linear convergence of the matrix splitting algorithm for the GLCP. Some numerical experiments are provided to show the validity of the obtained results.