#### Imene Touil, Djamel Benterki, A primal-dual interior-point method for the semidefinite programming problem based on a new kernel function, Vol. 2019 (2019), Article ID 25, pp. 1-17

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DOI: 10.23952/jnfa.2019.25

Received January 25, 2019; Accepted June 17, 2019; Published June 28, 2019

Abstract. The purpose of this paper is to improve the complexity of a large-update primal-dual interior point method for a semidefinite programming problem. We define a proximity function for the semidefinite programming problem based on a new parametric kernel function and prove that the worst-case iteration bound for the new correspondent algorithm is $\mathcal{O}\left( \sqrt{n}\left( \ln n\right) ^{\frac{pq+1}{pq}}\ln \frac{n}{\epsilon }\right),$ where $p,q\geq 1$.