Global Lipschitzian error bounds for semidefinite complementarity problems with emphasis on NCPs

Error bound theory play an important role in many mathematical programming problems. In this paper, we propose a new assumption condition under which we establish a global Lipshitzian error bound for the semidefinite complementarity problem (SDCP). As corollaries, two results involving the assumptions of strong monotonicity and BD-regularity are given. When the SDCP reduces to the nonlinear complementarity problem (NCP), our results strictly generalize the well-known error bound results which were established under the assumptions of strong monotonicity and uniform P-property. We also establish a new error bound for the NCP under BD-regularity and some R0-type condition.