چکیده
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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
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