一类具有全局收敛性质的共轭梯度法-论文.pdf

《一类具有全局收敛性质的共轭梯度法-论文.pdf》由会员上传分享，免费在线阅读，更多相关内容在应用文档-天天文库。

1、长江大学学报(自科版)。年。月号理上第u卷第期JournaofYangtzeUniversity(NatSciEdit)Mar．-2Z014VoOL11Nl(o)．‘7，ournai,ANewClassofNonlinearConjugateGradientMethodswithGlobalConvergencePropertiesCHENZhong(FreshmanEducati。nDepartment，YangtzeUniversity，HubeiJingzh。u434025)[Abstract3Nontinearconjugategradientmethodsha

2、veplayedanimportantroleinsolvinglargescaleuncon—strainedoDtimizati0nprob1ems，itischaracterizedbythesimplicityoftheiriterationandtheirlowmemorYre0uirements．Itiswe11-knownthatthedirectiongeneratedbyaconjugategradientmethodmaYbenotade—scentdirection．Inthispaper，anewclassofnonlinearconjugate

3、gradientmethodispresented’Itssearchdi-rection

4、sadescentdirectionfortheobjectivefunction．Iftheobjectivefunctionisdifferentiableanditsgradi—entLiDschitzcontinUOUs，thelinesearchsatisfiesstrongWolfecondition’theglobalconvergenceesults．established．[Keywords]conjugategradientmethod：linesearch；

5、globalconvergence；Hnconsrain。d。ptim。“[ChineseLibraryClassification]O241[Do~ntoDde]A[-ArticlelD]1673—1409(2o14)07—0001—041Intr0ductiOnLetnsconsidertheunconstrainedoptimizationproblem：min()(1)where厂(z)：R”Risasmoothnonlinearfunctionanditsgradientisdenotedbyg(z)一vf(x)·Ingen—era1thenonlinearc

6、onjugategradientmethodhasthefollowingform：Xk~-i—z+dk=0，1，2，⋯(2)whereisthecurrentiteratepoint；isastepsizeanddisthesearchdirection，whichisdefinedby：(3)一I一+一，忌≥1whereg一g(x)。Conjugategradientmethodsdifferintheirwayofdefiningthescalarparameter&．Inthelitera—tures，therehavebeenproposedseveralch

7、oicesfor／?kwhichgiverisetodistinctconjugategradientmeth—ods．Somewellknownformulasforaregivenasfollows：gg=lIg(-＼(一gH)一(g一g一1)d一1g(g女一g^一1)rd一1ThismethodsareknownasF1etcherandReevesmethod[，Polak—Ribiere—Polyakmethod[。]，HestenesandSteifelmethod[3]，andDaiandYuanmethod4。，respectively．If厂(z)is

8、strictlyaconvexquadraticfunction，allofthesemethodsundertheexactlinesearchhavefiniteconvergenceproper一[Receiveddata]2013—-i0——20[Fonngdationitem]NSFProject。fChinaGrant(61273179；11201039)；HubeiProVincia1DepartmentofEducatlonGrant(D20101304)。[Biography]CHENZhong(1965一)，male，