Complexity analysis of an interior-point algorithm for linear optimization based on a new proximity function.

Kernel functions play an important role in the complexity analysis of the interior point methods for linear optimization. In this paper, we present a primal-dual interior point method for linear optimization based on a new kernel function consisting of a trigonometric function in its barrier term. By simple analysis, we show that the feasible primal-dual interior point methods based on the new proposed kernel function enjoys $O\left (\sqrt {n}\left (\log {n}\right )^{2}\log \frac {n}{\epsilon }\right )$ worst case complexity result which improves the results obtained by El Ghami et al. (J Comput Appl Math 236:3613-3623, 2012) for the kernel functions with trigonometric barrier terms. [ABSTRACT FROM AUTHOR]