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

Kernel functions play an important role in the complexity analysis of interior point methods (IPMs) for linear optimization (LO). In this paper, interior-point algorithm LO based on a new parametric kernel function is proposed. By means some simple tools, we prove that primal-dual solving problems meets $ O\left(\sqrt{n} \log(n) \log(\frac{n}{\varepsilon}) \right) $, iteration bound large-update with special choice its parameters.