مشخصات پژوهش

In this paper, we propose a full-Newton step infeasible interior-point algorithm (IPA) for solving linear optimization problems based on a new kernel function (KF). The latter belongs to the newly introduced hyperbolic type (Guerdouh et al. in An effi- cient primal-dual interior point algorithm for linear optimization problems based on a novel parameterized kernel function with a hyperbolic barrier term, 2021; Touil and Chikouche in Acta Math Appl Sin Engl Ser 38:44–67, 2022; Touil and Chikouche in Filomat 34:3957–3969, 2020). Unlike feasible IPAs, our algorithm doesn’t require a feasible starting point. In each iteration, the new feasibility search directions are computed using the newly introduced hyperbolic KF whereas the centering search directions are obtained using the classical KF. A simple analysis for the primal-dual infeasible interior-point method (IIPM) based on the new KF shows that the iteration bound of the algorithm matches the currently best iteration bound for IIPMs. We con- solidate these theoretical results by performing some numerical experiments in which we compare our algorithm with the famous SeDuMi solver. To our knowledge, this is the first full-Newton step IIPM based on a KF with a hyperbolic barrier term