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.