|
Abstract
|
We propose a newlarge-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 Takács (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 Takács 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–Takács’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.
|