A polynomial-time weighted path-following interior-point algorithm for linear optimization

Abstract

In this paper, a weighted short-step primal-dual path-following interior-point algorithm for solving linear optimization (LO) is presented. The algorithm uses at each interior-point iteration a full-Newton step, thus no need to use line search, and the strategy of the central-path to obtain an [Formula: see text]-approximated solution of LO. We show that the algorithm yields the iteration bound, namely, [Formula: see text]. This bound is currently the best iteration bound for LO. Finally, some numerical results are reported in order to analyze the efficiency of the proposed algorithm.