Warm start of interior point methods for multicommodity network flow problem

In this paper, we present a methodology for solving the multicommodity network flow problems using interior point methods. In our method, the minimum cost network flow problem extracted from the given multicommodity network flow problem is solved and primal–dual barrier method in which normal equations are solved partially using preconditioned conjugate gradient method. Based on the solution of the minimum cost network flow problem, a warm-start point is obtained from which Castro's specialized interior point method for multicommodity network flow problem starts. In the computational experiments, the effectiveness of our methodology is shown.