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A large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function

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Abstract

In this paper, we present a large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. The proposed function is strongly convex. It is not self-regular function and also the usual logarithmic function. The goal of this paper is to investigate such a kernel function and show that the algorithm has favorable complexity bound in terms of the elegant analytic properties of the kernel function. The complexity bound is shown to be \(O\left( {\sqrt n \left( {\log n} \right)^2 \log \frac{n} {\varepsilon }} \right)\). This bound is better than that by the classical primal-dual interior-point methods based on logarithmic barrier function and recent kernel functions introduced by some authors in optimization fields. Some computational results have been provided.

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Authors and Affiliations

  1. College of Science, China Three Gorges University, Yichang, 443002, P. R. China

    Ming Wang Zhang

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  1. Ming Wang Zhang
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Correspondence to Ming Wang Zhang.

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Supported by Natural Science Foundation of Hubei Province of China (Grant No. 2008CDZ047)

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Zhang, M.W. A large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. Acta. Math. Sin.-English Ser. 28, 2313–2328 (2012). https://doi.org/10.1007/s10114-012-0194-0

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  • DOI: https://doi.org/10.1007/s10114-012-0194-0

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