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Analysis of complexity of primal-dual interior-point algorithms based on a new kernel function for linear optimization

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  • Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithm. In this paper, a new kernel function which its barrier term is integral type is proposed. We study the properties of the new kernel function, and give a primal-dual interior-point algorithm for solving linear optimization based on the new kernel function. Polynomial complexity of algorithm is analyzed. The iteration bounds both for large-update and for small-update methods are obtained, respectively. The iteration bound for small-update method is the best known complexity bound.
    Mathematics Subject Classification: Primary: 90C05, 90C51.


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    Y. Q. Bai, J. Guo and C. Roos, A new kernel function yielding the best known iteration bounds for primal-dual interior-point algorithms, Acta Mathematica Sinica English Series, 25 (2009), 2169-2178.doi: 10.1007/s10114-009-6457-8.


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