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, algorithms can be divided into two main groups, short-step, and methods. practice, variants perform better, but usually, better theoretical complexity achieved short-step One of exceptions is large-update Ai Zhang. The wide neighborhood characteristics presented are based their approach. addition, use algebraic equivalent transformation technique Darvay to determine modified search directions our method. We show that convergent has best known iteration variants. present numerical results compare performance with previously introduced Ai-Zhang type set programming test problems from Netlib library.