A new wide neighborhood primal-dual second-order corrector algorithm for linear optimization

Abstract

We propose a new large-step primal-dual second-order corrector interior-point method for linear optimization. At each iteration, our method uses the new wide neighborhood introduced by Darvay and Takacs (Cent Eur J Oper Res 26(3):551–563, 2018. https://doi.org/10.1007/s10100-018-0524-0 ). In this paper we would like to improve the directions proposed by Darvay and Takacs by adding a second-order corrector direction. The corrector step is multiplied by the square of the step length in the expression of the new iterate. To our best knowledge, this is the first primal-dual second-order corrector interior-point algorithm based on Darvay–Takacs’s new wide neighborhood, which has the same complexity as the best short-step algorithms for linear optimization. Finally, numerical experiments show that the proposed algorithm is efficient and reliable.