A wide neighbourhood interior-point method with iteration-complexity bound for semidefinite programming

In this article we propose a new class of primal-dual path-following interior-point algorithms for semidefinite programming (SDP). Each iterate always follows the usual wide neighbourhood , not necessarily remaining within it, but must stay within the wider neighbourhood . We show that the algorithm has iteration-complexity bound which is better than that of the usual wide neighbourhood algorithm O(nL). It is the best result in regard to iteration-complexity bound in the context of path-following method for SDP.

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