<p style='text-indent:20px;'>Kernel functions play an important role in the complexity analysis of the interior point methods (IPMs) for linear optimization (LO). In this paper, an interior-point algorithm for LO based on a new parametric kernel function is proposed. By means of some simple analysis tools, we prove that the primal-dual interior-point algorithm for solving LO problems meets <inline-formula><tex-math id="M1">\begin{document}$ O\left(\sqrt{n} \log(n) \log(\frac{n}{\varepsilon}) \right) $\end{document}</tex-math></inline-formula>, iteration complexity bound for large-update methods with the special choice of its parameters.</p>

In this paper, we propose a large-update primal-dual interior point algorithm for linear optimization. The method is based on a new class of kernel functions which differs from the existing kernel functions in which it has a double barrier term. The investigation according to it yields the best known iteration bound O( √ n log(n) log( n ε )) for large-update algorithm with the special choice of its parameter m and thus improves the iteration bound obtained in Bai et al. [2] for large-update algorithm. 2020 MSC: 90C05, 90C51, 90C31