Primal-Dual IPMS for Semidefinite Optimization Based on Finite Barrier Functions

In this paper we extend the results obtained for a class of finite kernel functions by Y.Q. Bai M. El Ghami and C.Roos published in SIAM Journal of Optimization for linear optimization to semidefinite optimization. We show that the iteration bound for primal dual methods is O(\sqrt{n}\log{n}\log{\frac{n}{\epsilon}}), for large-update methods and O(\sqrt{n}\log\frac{n}{\epsilon}), for small-update methods. The iteration complexity obtained for semidefinite programming is the same as the best bound for primal-dual interior point methods in linear optimization.