Geodesic
A new parameterized logarithmic kernel function for linear optimization with a double barrier term yielding the best known iteration bound
Communications in Mathematics, Tome 28 (2020) no. 1, pp. 27-41.

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In this paper, we propose a large-update primal-dual interior point algorithm for linear optimization. The method is based on a new class of kernel functions which differs from the existing kernel functions in which it has a double barrier term. The investigation according to it yields the best known iteration bound $O(\sqrt {n} \log (n) \log (\frac {n}{\varepsilon }) )$ for large-update algorithm with the special choice of its parameter $m$ and thus improves the iteration bound obtained in Bai et al.~\cite {El Ghami2004} for large-update algorithm.
Classification : 90C05, 90C31, 90C51
Keywords: Linear optimization; Kernel function; Interior point methods; Complexity bound 
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     title = {A new parameterized logarithmic kernel function for linear optimization with a double barrier term yielding the best known iteration bound},
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Ayache, Benhadid; Khaled, Saoudi. A new parameterized logarithmic kernel function for linear optimization with a double barrier term yielding the best known iteration bound. Communications in Mathematics, Tome 28 (2020) no. 1, pp. 27-41. http://geodesic.mathdoc.fr/item/COMIM_2020__28_1_a2/