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Abstract

The aim of this work is to improve the complexity result for the large-update method. First, we present a new bi-parametric kernel function with a hyperbolic barrier term. Then using simple tools, we show that the complexity bound of the algorithm based on the proposed kernel function for the large-update method is $\mathcal O\big(\sqrt {n}\log n\log \frac{n}{\epsilon}\big)$ iterations. This result coincides with the current best-known iteration bounds for interior point methods based on all existing types of kernel functions. To illustrate the effectiveness of the algorithm developed, we give some numerical tests.