资源描述：
《求解无约束问题的一个杂交共轭梯度法》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、求解无约束问题的一个杂交共轭梯度法第32卷增刊2007年9月广西大学(自然科学版)JournalofGuangxiUniversity(NatSciEd)文章编号:1001—7445(2007)增一0239?05Vo1.32,SuPSept..2007AhybridconjugategradientmethodforunconstrainedoptimizationWEIZeng—xin,DENGXiao—hong,ZHOUYa—qun(Co11egeofMathematicsandInformation
2、Science.GuangxiUniversity?Nanning530004?Chi")Abstract:AnewhybridconjugatemethodbasedonPRPmethodisproposed?Thecong"propystudied.Numerica1resultsshowthatitiseffcient.Keyw.rds:unc.nstraned.ptimizati.n;c.njugategradientemeth.d;w.Ifelinesearchc.nditi.ns;suffic
3、descentproperty;globalconvergence?CLCnumber:O221.2Documentcode:A1IntroductionTheconjugategradientmethodisdesignedtoso!Vethefollowingunconstrainednol;".optimizationproblemmin厂(),(])ewhere厂:R一Risasmooth,nonlinearfunctionwhosegradientwillbedenotedbyg?Theiter
4、嚣÷Veforn1u1aoftheconjugategradientmethodisgivenbyz+1一z十,(2)where}isastep—length,andd^isthesearchdirectiondefinedby一』--gk,一U'(3)"一l一士d一.,≥1,whereisasca1arandg^denotesg(^).rhereares.meram.usformu1asf.rilk,suchasp^,,p^D,p.,p^,thedetailanalysisforthesemethods
5、arein[3～8]?lnpaper[1],theauthorproposedaneffcientformulafor,whichisdenotedby,itisiustthesameasHSmethodifexactlinesearchconditionisused.ForPRPmethod?thoughtperformsverywellwithWolfelinesearch,buttheconvergencypropertystillcannotbeproVedeVe'undertheassumpti
6、onofsuffcientdescentproperty㈨.In[10],theauthorproposedahybridconjugategradientmethod,inwhich—mx(0'n1in(,FR)).Anotherauthorin[2]modifiedthishybridconjugate!nethodandobtaindbnumericalresult.1nrecentyears,someotherauthorshavedonemuchWOtk.nstudyingCOnjugaegra
7、enttypemethodandtheyobtainedgoodresuhsL?Inthispaper,weproposeanewhybridconjugatemethod,,ve-】sethefollowingformula.obtain:Receiveddate:2007—04—21Fundationitem:SupportedbyGuangxiNSF(0542043)Bi.graphy:WEIZeng-xin(1962一),Male,Zhua"gPeople,Gua"gxiProvince,Prof
8、ess.r.fGuangxiUniversity240广西大学(自然科学版)第32卷where--=max(0,min(flkp,)),'一+2dk-,llg一ll'yk—gI—gI一1?WeuseboththeweakWolfeandstronglinesearchconditionsin(WWP):厂(zj+fId)--f(xI)≤gTdI,g(xI+fIdI)dI≥ag[dI.strongWolfecondition(S
