Analyticity of the central path at the boundary point in semidefinite programming

In this paper we study the limiting behavior of the central path for semidefinite programming (SDP). We show that the central path is an analytic function of the barrier parameter even at the limit point, provided that the semidefinite program has a strictly complementary solution. A consequence of this property is that the derivatives – of any order – of the central path have finite limits as the barrier parameter goes to zero.