In this paper, error bounds for nonlinear semidefinite optimization problem is considered. We assume the second order sufficient 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 satisfies the shifted complementarity condition along with the MFCQ condition and the second order sufficient condition. Finally we gather these results and obtain the upper and lower local error bounds for the primal-dual pair.
Citation
Technical report Oct. 2016 NTT DATA Mathematical Systems Inc. 35 Shinanomachi, Shinjuku-ku, Tokyo, Japan