An extension for identifying search directions for interior-point methods in linear optimization

Abstract

In this paper, based on the transformation [Formula: see text] introduced by Darvay and Takács [New method for determining search directions for interior-point algorithms in linear optimization, Optim. Lett. 12(5) (2018) 1099–1116], we present a full-Newton step interior-point method for linear optimization. They consider the case [Formula: see text]. Here, we extend this to the case [Formula: see text] to obtain our search directions. We show that the iterates lie in the neighborhood of the local quadratic convergence of the proximity measure. Finally, the polynomial complexity of the proposed algorithm is proved.