Abstract
In this paper, we propose a primal-dual interior point method for linear optimization (LO) based on a new parameterized kernel function. The proposed kernel function is a generalization of the one used recently in Bai et al. (SIAM J Optim 15:101–128, 2004) for LO. The investigation according to it yields the best known iteration bound \(O\left( \sqrt{n} \log n \log \frac{n}{\epsilon }\right) \) for large-update algorithm and thus improves the iteration bound obtained in Bai et al. (SIAM J Optim 15:101–128, 2004) for large-update algorithm. Finally, we present few numerical results to demonstrate the efficiency of the proposed algorithm.
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Achache, M. A new parameterized kernel function for LO yielding the best known iteration bound for a large-update interior point algorithm. Afr. Mat. 27, 591–601 (2016). https://doi.org/10.1007/s13370-015-0363-2
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DOI: https://doi.org/10.1007/s13370-015-0363-2