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A primal-dual interior-point algorithm for symmetric optimization based on a new kernel function with trigonometric barrier term yielding the best known iteration bounds

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Abstract

Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithms for solving symmetric optimization problems. In this paper we present a new kernel function for which interior point method yields iteration bounds \({\mathcal {O}}(\sqrt{r}\log r\log \frac{r}{\epsilon })\) and \({\mathcal {O}}(\sqrt{r}\log \frac{r}{\epsilon })\) for large-and small-update methods, respectively, which matches currently the best known bounds for such methods.

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  1. Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Islamic Republic of Iran

    B. Kheirfam

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  1. B. Kheirfam
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Kheirfam, B. A primal-dual interior-point algorithm for symmetric optimization based on a new kernel function with trigonometric barrier term yielding the best known iteration bounds. Afr. Mat. 28, 389–406 (2017). https://doi.org/10.1007/s13370-016-0455-7

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  • DOI: https://doi.org/10.1007/s13370-016-0455-7

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