A long-step second-order corrector interior point algorithm for linear optimization based on the algebraic equivalent transformation

Abstract

In this paper, we present a new large-step primal-dual second-order corrector interior-point algorithm for linear optimization. This algorithm is based on the Nagy-Varga neighborhood of the central path, which uses the algebraic equivalent transformation strategy of Darvay et al. to determine the search directions. In addition, our method uses a second-order corrector direction in each iteration. The iterates remain in the proposed neighborhood by taking the largest possible step lengths along the search directions. We show that the new long-step algorithm is convergent and has the same complexity as the best short-step algorithms for linear optimization. To the best of our knowledge this is the first primal-dual second-order corrector interior-point algorithm that uses a different neighborhood from those available in the literature. Finally, numerical experiments show that the proposed algorithm is efficient and competitive.