Geodesic
An interior-point algorithm for semidefinite least-squares problems
Applications of Mathematics, Tome 67 (2022) no. 3, pp. 371-391.

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We propose a feasible primal-dual path-following interior-point algorithm for semidefinite least squares problems (SDLS). At each iteration, the algorithm uses only full Nesterov-Todd steps with the advantage that no line search is required. Under new appropriate choices of the parameter $\beta $ which defines the size of the neighborhood of the central-path and of the parameter $\theta $ which determines the rate of decrease of the barrier parameter, we show that the proposed algorithm is well defined and converges to the optimal solution of SDLS. Moreover, we obtain the currently best known iteration bound for the algorithm with a short-update method, namely, $\mathcal {O}(\sqrt {n}\log (n/\epsilon ))$. Finally, we report some numerical results to illustrate the efficiency of our proposed algorithm.
DOI : 10.21136/AM.2021.0217-20
Classification : 65K05, 90C22, 90C25, 90C51
Keywords: semidefinite least-squares problem; interior-point method; polynomial complexity 
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Daili, Chafia; Achache, Mohamed. An interior-point algorithm for semidefinite least-squares problems. Applications of Mathematics, Tome 67 (2022) no. 3, pp. 371-391. doi : 10.21136/AM.2021.0217-20. http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0217-20/

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