A wide neighborhood interior-point algorithm for linear optimization based on a specific kernel function

Abstract

This paper presents an interior point algorithm for solving linear optimization problems in a wide neighborhood of the central path introduced by Ai and Zhang (SIAM J Optim 16:400–417, 2005). In each iteration, the algorithm computes the new search directions by using a specific kernel function. The convergence of the algorithm is shown and it is proved that the algorithm has the same iteration bound as the best short-step algorithms. We demonstrate the computational efficiency of the proposed algorithm by testing some Netlib problems in standard form. To best our knowledge, this is the first wide neighborhood path-following interior-point method with the same complexity as the best small neighborhood path-following interior-point methods that uses the kernel function.