A feasible primal-dual interior point method for linear semidefinite programming

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• 作者：Imene Touil^a ; ^{i_touil@yahoo.fr" class="auth_mail" title="E-mail the corresponding author} ; Djamel Benterki^b ; Adnan Yassine^c ; ^d ; ^e
• 关键词：90C22 ; 90C51
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：312
• 期：Complete
• 页码：216-230
• 全文大小：465 K

文摘

In this paper, we consider a feasible primal–dual interior point method for linear semidefinite programming problem (SDP)$\left(SDP\right)$ based on Alizadeh–Haeberly–Overton (AHO) direction (Monteiro, 1997). Firstly, and by a new and simple technique, we establish the existence and uniqueness of optimal solution of the perturbed problem 131b583" title="Click to view the MathML source">(SDP)_μ${\left(SDP\right)}_{\mu }$ and its convergence to optimal solution of (SDP)$\left(SDP\right)$. Next, we present new different alternatives to calculate the displacement step. After, we establish the convergence of the obtained algorithm and we show that its complexity is $\mathcal{O}(\sqrt{n}ln\left[{\epsilon }^{-1}\left(〈X^0,S^0〉\right)\right])$. Finally, we present some numerical simulations which show the effectiveness of the algorithm developed in this work.