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Primal-dual interior-point algorithm for semidefinite optimization based on a new kernel function with trigonometric barrier term

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Abstract

In this paper we propose primal-dual interior-point algorithms for semidefinite optimization problems based on a new kernel function with a trigonometric barrier term. We show that the iteration bounds are \(O(\sqrt{n}\log(\frac{n}{\epsilon}))\) for small-update methods and \(O(n^{\frac{3}{4}}\log(\frac{n}{\epsilon}))\) for large-update, respectively. The resulting bound is better than the classical kernel function. For small-update, the iteration complexity is the best known bound for such methods.

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  1. Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, Iran

    Behrouz Kheirfam

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  1. Behrouz Kheirfam
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Kheirfam, B. Primal-dual interior-point algorithm for semidefinite optimization based on a new kernel function with trigonometric barrier term. Numer Algor 61, 659–680 (2012). https://doi.org/10.1007/s11075-012-9557-y

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