A sensitivity result for semidefinite programs. (Q1417590)

The authors consider the perturbation of solutions of linear semidefinite problems subjected to small changes of the data. A self-contained proof of the differentiability of unique and strictly complementary solutions is given. Furthermore a new characterization of the derivatives of the solution map as solutions of a nonsingular system of linear equations is presented. The last section of the paper contains some examples illustrating that the differentiability property proved cannot be generalized straightforwardly to more general convex programs in conic form.