Initialization in semidefinite programming via a self-dual skew-symmetric embedding

The formulation of interior point algorithms for semide nite programming has become an active research area, following the success of the methods for large{ scale linear programming. Many interior point methods for linear programming have now been extended to the more general semide nite case, but the initialization problem remained unsolved. In this paper we show that the initialization strategy of embedding the problem in a self{dual skew{symmetric problem can also be extended to the semi{de nite case. This way the initialization problem of semi{de nite problems is solved. This method also provides solution for the initialization of quadratic programs and it is applicable to more general convex problems with conic formulation.