Geodesic
Full-Newton step infeasible interior-point algorithm for SDO problems
Kybernetika, Tome 48 (2012) no. 5, pp. 907-923

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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.
Classification : 90C05, 90C51
Keywords: semidefinite optimization; infeasible interior-point method; primal-dual method; polynomial complexity; Newton-step; optimal solutions 
@article{KYB_2012__48_5_a5,
     author = {Mansouri, Hossein},
     title = {Full-Newton step infeasible interior-point algorithm for {SDO} problems},
     journal = {Kybernetika},
     pages = {907--923},
     publisher = {mathdoc},
     volume = {48},
     number = {5},
     year = {2012},
     mrnumber = {3086859},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_5_a5/}
}
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Mansouri, Hossein. Full-Newton step infeasible interior-point algorithm for SDO problems. Kybernetika, Tome 48 (2012) no. 5, pp. 907-923. http://geodesic.mathdoc.fr/item/KYB_2012__48_5_a5/