### An Interior Point Algorithm for Solving Linear Optimization Problems Using a New Trigonometric Kernel Function

#### Abstract

In this paper, a primal-dual interior-point algorithm for solving linear optimization problems based on a new

kernel function with a trigonometric barrier term which

is not only used for determining the search directions but also for measuring the

distance between the given iterate and the $\mu$-center for the algorithm is proposed.

Using some simple analysis tools and prove that our algorithm

based on the new proposed trigonometric kernel function meets

$O\left(\sqrt{n}\log n\log \frac{n}{\varepsilon}\right)$ and $O\left(\sqrt{n}\log \frac{n}{\varepsilon}\right)$ as the

worst case complexity bounds for large and small-update methods.

Finally, some numerical results of performing our algorithm are presented.

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