An adaptive-step primal-dual interior point algorithm for linear optimization

Abstract

A common feature shared by most practical algorithms in interior point methods is the use of Mehrotra’s predictor–corrector algorithm in [S. Mehrotra, On the implementation of a (primal-dual) interior point method, SIAM Journal on Optimization 2 (1992) 575–601.] where the predictor step is never performed but it is used only to calculate an adaptive update, and thus instead of a predictor and a corrector centering step, a single Newton step is made toward the adaptively chosen target. In this paper we propose a new adaptive single-step large-update primal-dual interior point algorithm with wide neighborhood for linear optimization(LO) problems based on the simple kernel function which is first defined in [Y.Q. Bai, C. Roos, A primal-dual interior-point method based on a new kernel function with linear growth rate, in: Proceedings of Industrial Optimization Symposium and Optimization Day, Nov., 2002]. We show that the algorithm has O ( q n τ log ( n / ε ) ) complexity which is similar to the one in the above-mentioned reference.