求解对称锥互补问题的一种非精确光滑牛顿方法.pdf

《求解对称锥互补问题的一种非精确光滑牛顿方法.pdf》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、CHINESEJoURNALVo1．32No．1Feb．20150FENGINEERINGMATHEMATICSdoi：10．3969／j．issn．1005—3085．2015．01．013ArticleID：1005—·3085(2015)01·0131--14AnInexactSmoothingNewtonMethodforSolvingSymmetricConeComplementarityProblem木RUIShao-ping(SchoolofMathematicalScience，HuaibeiNormal

2、University,Huaibei235000)Abstract：Inthispaper，weproposeaninexactsmoothingmethodforsolvingsymmetricconecomplementarityproblembasedonaone—parametricclassofsmoothingfunctionwhichcontainstheFBsmoothingfunctionandtheCHKSsmoothingfunctionasspecialcases．Ateachiteration，

3、weusetheGMRESiterativesolvertoobtainanapproximatesolutiontothegeneratedsmoothingNewtonlinearsystem．Undersuitableconditions，weobtainglobalconvergenceandlocalsuperlinearconvergenceoftheproposedalgorithm．Numericalresultsindicatethattheproposedalgorithmisefectiveforl

4、arge-scaleproblem．Keywords：symmetricconecomplementarityproblem；inexactsmoothingalgorithm；Euclid-earlJordanalgebra；large—scaleproblemClassification：AMS(2000)90C33CLCnumber：0224Documentcode：A1IntroductionInthispaper，weareinterestedinthefollowingsymmetricconecomplem

5、entarityproblemfSCCP)：findvectorsX，Y∈Vsuchthat∈JlC，=F(x)∈，(，)=0，(1)whereVisann—dimensionalEuclideanspace，cVisasymmetriccone，(·，·)denotestheEuclideaninnerproduct，andFisacontinuouslydiferentiablemapping．Prob-lem(1)includesthesemidefinitecomplementarityproblem(SDCP)

6、，thesecond-orderconecomplementarityproblem(SOCCP)andthenonlinearcomplementarityproblem(NCP)asspecialcases．Duetoitswideapplications，manynumericalmethodsforsolvingSCCP(1)havebeenproposed[卜引Recently,motivatedbysuccessfulapplicationsofsmoothingmeth-．odsinsolutionofNC

7、P，SOCCPandSDCP，someresearcheshavebeenstronginterestedReceived：06Sep2013．Biography：RuiShaoping(Bornin1978)，Male，Doctor，AssociateProfes-Accepted：07Jan2014．sor．Researchfield：optimizationtheoryandalgorithm．*Foundationitem：TheNaturalScienceFoundationofEducationDepartm

8、entofAnhuiProvince(KJ2013A235)．132CHINESEJoURNAL0FENGINEERINGMATHEMATICSVoL．32instudyingthismethodforsolvingSCCP．However，inmostsmoothingmethod，eachiterationnee