#### Zahra Moaberfard, Sajad Fathi-Hafshejani, Alireza Fakharzadeh J., An interior-point method for linear optimization based on a trigonometric kernel function, Vol. 2019 (2019), Article ID 46, pp. 1-17

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DOI: 10.23952/jnfa.2019.46

Received August 31, 2019; Accepted November 24, 2019; Published December 2, 2019.

Abstract. In this paper, we propose a large-update primal-dual interior point algorithm for linear optimization problems based on a new kernel function with a trigonometric barrier term. By means of some simple analysis tools, we prove that the interior-point algorithm based on the new proposed kernel function meets $O\left(\sqrt{n}\log n\log \frac{n}{\varepsilon}\right)$ as the worst-case complexity bound for the large-update method, which coincides with the best-known complexity result for large-update method. Finally, some numerical results of performing the algorithm are presented.