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| Paper IPM / M / 14729 |
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| Abstract: | |
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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
â1−[1/(O\br√r)]â, âwhere r is the rank of theâ
âassociated Euclidean Jordan algebrasâ. âIn particularâ, âtheâ
âcomplexity bound is O\br√r logε−1â,
âwhere ε > 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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