Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21287120220601A second-order corrector wide neighborhood infeasible interior-point method for linear optimization based on a specific kernel function29441417310.22049/cco.2021.27044.1185ENBehrouz KheirfamMathematicsorcid.org/0000-0001-7928-2618Afsaneh NasrollahDepartment of Mathematics, Azarbaijan Shahid Madani UniversityJournal Article20201210In this paper, we present a second-order corrector infeasible<br />interior-point method for linear optimization in a large<br />neighborhood of the central path. The innovation of our method is to<br />calculate the predictor directions using a specific kernel function<br />instead of the logarithmic barrier function. We decompose the<br />predictor direction induced by the kernel function to two orthogonal<br />directions of the corresponding to the negative and positive<br />component of the right-hand side vector of the centering equation.<br />The method then considers the new point as a linear combination of<br />these directions along with a second-order corrector direction. The<br />convergence analysis of the proposed method is investigated and it<br />is proved that the complexity bound is<br />$\mathcal{O}(n^{\frac{5}{4}}\log\varepsilon^{-1})$.https://comb-opt.azaruniv.ac.ir/article_14173_be36f496696d9c17ddbe54d1b26b21db.pdf