ON A GLOBAL PROJECTION-TYPE ERROR BOUND FOR THE LINEAR COMPLEMENTARITY-PROBLEM

We consider a projection-type error bound for the linear complementari ty 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 necess ary. 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 ne cessary and sufficient conditions on M for this error bound to hold gl obally, independent of q. These conditions are closely related to M be ing Lipschitzian. We also discuss application of our result to the aff ine variational inequality problem. (C) Elsevier Science Inc., 1997.