Complexity analysis of an interior-point algorithm for linear optimization based on a new parametric kernel function with a double barrier term

Abstract

<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>