# A second-order corrector wide neighborhood infeasible interior-point method for linear optimization based on a specific kernel function

Document Type : Original paper

Authors

1 Mathematics

2 Department of Mathematics, Azarbaijan Shahid Madani University

Abstract

In this paper, we present a second-order corrector infeasible
interior-point method for linear optimization in a large
neighborhood of the central path. The innovation of our method is to
calculate the predictor directions using a specific kernel function
instead of the logarithmic barrier function. We decompose the
predictor direction induced by the kernel function to two orthogonal
directions of the corresponding to the negative and positive
component of the right-hand side vector of the centering equation.
The method then considers the new point as a linear combination of
these directions along with a second-order corrector direction. The
convergence analysis of the proposed method is investigated and it
is proved that the complexity bound is
$\mathcal{O}(n^{\frac{5}{4}}\log\varepsilon^{-1})$.

Keywords

Main Subjects

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