Hossein Mansouri

# Abstract:

In this paper we propose a primal-dual path-following interior-point algorithm for semidefinite optimization. The algorithm constructs strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Each main step of the algorithm consists of a feasibility step and several centering steps. At each iteration, we use only full-Newton step. Moreover, we use a more natural feasibility step, which targets at the $\mu^+$-center. The iteration bound of the algorithm coincides with the currently best iteration bound for semidefinite optimization problems.

# Keywords:

polynomial complexity, semidefinite optimization, infeasible interior-point method, primal-dual method, Newton-step, optimal solutions

90C05, 90C51

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