“School of Mathematics”
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Paper IPM / M / 16446  


Abstract:  
In this paperâ, âwe propose a predictorcorrector interiorpoint method for symmetricâ
âcone optimizationâ. âThe proposed algorithm is based on a newâ
âonenorm neighborhoodâ, âwhich is an even wider neighborhood than aâ
âgiven negative infinity neighborhoodâ. âThe convergence is shownâ
âfor a commutative class of search directionsâ, âwhich includes theâ
âNesterovTodd direction and the xs and sx directionsâ. âWe showâ
âthat the algorithm has O\br√r\br\cond(G)^{1/4}logε^{−1} iteration complexity bound which is betterâ
âthan that of the usual wide neighborhood algorithmâ
âO\brr√{\cond(G)}logε^{−1}â. âTo ourâ
âknowledgeâ, âthese are the best complexity results obtained so farâ
âfor the solution of SCOâ. âWe prove thatâ,
âbesides the predictor stepsâ, âeach corrector step also reduces the duality gap by a rate of 1−[1/(O\br√r)]â.
âFinallyâ, ânumerical experiments showthat the proposed algorithm is efficientâ
âand reliableâ.
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