A Sensitivity Result for Semidefinite Programs

We study the sensitivity of strictly complementary solutions of linear semidefinite programs when the data is subject to small arbitrary changes. We show that the perturbations of the solutions are differentiable functions of the perturbations of the data, and we characterize the derivatives. 

This result improves upon earlier results that were established by Robinson for more general cone programs. We also show why our result does not apply to such more general cone programs.