An Efficient Interior Point Method for Linear Optimization Using Modified Newton Method

Interior point methods are one of the popular iterative approaches for solving optimization problems. Search direction plays a vital role in the performance of the interior point methods. This paper uses a modification to the Newton method and proposes a new way to find the search direction. We introduce a two-step interior point algorithm for solving linear optimization problems based on the new search direction. We present theoretical results for the convergence of the algorithm. Finally, we evaluate the algorithm on some test problems from the Netlib collection and show that the proposed algorithm reduces the number of iterations and CPU time by \(30.97\%\) and \(20.46\%\) , respectively.