A New Long-Step Path-Following Interior-Point Method with O(vnL) Iteration-Complexity Bound for Semidefinite Programming

In this paper we propose a new class of primal-dual path-following interior point algorithms for semidefinite programming. Each iterate is always following the usual wide neighborhood N_¿ ^-(¿), not necessary stay within it, but must stay within the wider neighborhood N(¿,ß). We show that the algorithm has O(¿nL) iteration complexity bound which is better than that of usual wide neighborhood algorithm O(nL). It is the best result in regard the iteration complexity bound in the context of path-following method for semidefinite programming.