Error bounds for nonlinear semide nite optimization

In this paper, error bounds for nonlinear semide nite optimization problem is considered. We assume the second order su cient condition, the strict complementarity condition and the MFCQ condition at the KKT point. The nondegeneracy condition is not assumed in this paper. Therefore the Jacobian operator of the equality part of the KKT conditions is not assumed to be invertible. We derive lower bounds for the primal and dual distances to the solution set when the primal variable is close to the solution set. Then a global error bound of the dual distance to the solution set is obtained assuming the MFCQ condition and the strict complementarity condition. An error bound for the primal variable is given when the primal-dual pair is close to the solution set, and approximately satis es the shifted complementarity condition along with the MFCQ condition and the second order su cient condition. Finally we gather these results and obtain the upper and lower local error bounds for the primal-dual pair.