A new long-step interior point algorithm for linear programming based on the algebraic equivalent transformation

Abstract

In this paper, we investigate a new primal-dual long-step interior point algorithm for linear optimization. Based on the step size, interior point algorithms can be divided into two main groups, short-step, and long-step methods. In practice, long-step variants perform better, but usually, a better theoretical complexity can be achieved for the short-step methods. One of the exceptions is the large-update algorithm of Ai and Zhang. The new wide neighborhood and the main characteristics of the presented algorithm are based on their approach. In addition, we use the algebraic equivalent transformation technique of Darvay to determine new modified search directions for our method. We show that the new long-step algorithm is convergent and has the best known iteration complexity of short-step variants. We present our numerical results and compare the performance of our algorithm with two previously introduced Ai-Zhang type interior point algorithms on a set of linear programming test problems from the Netlib library.