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Linear optimization; Kernel function; Interior point methods; Complexity bound
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.
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