Abstract
In this paper, we present a large-update primal-dual interior-point method for symmetric cone optimization (SCO) based on a new kernel function, which determines both search directions and the proximity measure between the iterate and the center path. The kernel function is neither a self-regular function nor the usual logarithmic kernel function. Besides, by using Euclidean Jordan algebraic techniques, we achieve the favorable iteration complexity \(O(\sqrt r (\log r)^2 \log (r/\varepsilon ))\), which is as good as the convex quadratic semi-definite optimization analogue.
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Foundation item: Supported by the Natural Science Foundation of Hubei Province (2008CDZD47)
Biography: ZHAO Dequan, female, Master, research direction: optimization theory and its application.
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Zhao, D., Zhang, M. Kernel function-based primal-dual interior-point methods for symmetric cones optimization. Wuhan Univ. J. Nat. Sci. 19, 461–468 (2014). https://doi.org/10.1007/s11859-014-1040-2
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DOI: https://doi.org/10.1007/s11859-014-1040-2