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âIn this paper,we propose a new predictor-corrector interior-pointâ
âmethod for symmetric cone programmingâ. âThis algorithm is based onâ
âa wide neighborhood and the Nesterov-Todd directionâ. âWe proveâ
âthatâ, âbesides the predictor stepsâ, âeach corrector step alsoâ
âreduces the duality gap by a rate ofâ
â$1-\frac{1}{\mbox{O}\br{\sqrt{r}}}$â, âwhere $r$ is the rank of theâ
âassociated Euclidean Jordan algebrasâ. âIn particularâ, âtheâ
âcomplexity bound is $\mbox{O}\br{\sqrt{r} \log \varepsilon^{-1}}$â,
âwhere $\varepsilon>0$ is a given toleranceâ. âTo our knowledgeâ,
âthis is the best complexity result obtained so far forâ
âinterior-point methods with a wide neighborhood over symmetricâ
âconesâ. âThe numerical results show that the proposed algorithm is effectiveâ.
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