On a global projection-type error bound for the linear complementarity problem Original Research Article

We consider a projection-type error bound for the linear complementarity problem involving a matrix M and vector q. First, we show that the Mangasarian-Ren sufficient condition on M for this error bound to hold globally, for all q such that the problem is solvable, is also necessary. Second, we derive necessary and sufficient conditions on M and q for this error bound to hold globally, thus extending a result of Luo and Tseng which in addition assumes M is psd-plus. Third, we derive necessary and sufficient conditions on M for this error bound to hold globally, independent of q. These conditions are closely related to M being Lipschitzian. We also discuss application of our result to the affine variational inequality problem.