半光滑方程組的牛頓類方法.pdf

1、上海師范大學碩士學位論文半光滑方程組的牛頓類方法姓名：羅娜申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：朱德通20070401英文摘要AbstractOptimization，whichmakesresearchonhowtofindtheoptimalsolutionamongmanyfeasibleprojects，iswidelyappliedinmanyfieldssuchasfinance，trade，managementands

2、cientificresearchHowtOsolvethesystemofnonlinearequationsisanimportantcomponentofoptimizationAclassicalalgorithmfortheproblemisNewton’SmethodThemethodisatwaetivebecauseitconvergesrapidlyforanysufficientlygoodinitialpointX

3、0Howeversolvingasystemoflinearequations(theNewtOnequations)exactlyateachstageCallbeexpensiveifthenumberofunknownsislargeandmaynotbejustifiedwhenzkisfarfromasolufionButthedrawbacksCanbeovercometOsomeextentifwesolvedlinear

4、equationsinexactlyandusingaffinetransformationwillimprovetheI弓sIlltandthefeasibilitySoweproposeallaffineinexactNewtonmethodForsolvingboundconstrainedsemismoothequations。aNewton—likemethodwithprojec—fionisproposedInordert

5、Ogeneratefeasibleiterates，weintroduceNewtonlikemethodthatisaugmentedbytheprojectionontOfeasiblesetItisprovedthattheadditionalprojectiondoesnotaffectthelocalsuperlinearconvergencespeedInordertoobtainglobalconvergencewedes

6、cribeanalgorithmcalledaffinescalinginteriormethod11地basicideaistequireastepback—trackingalongtheNewton—likestepbythestrictinteriorfeasibilityandlinesearchtechnique，becauselinesearchisanimportanttechniquewhichCanobtainglo

7、balconvergenceT1leframeofthepaperisfollowing：Inchapter2，anaffineinexactNewtonmethodforthesystemofnonlinearequationsisproposedwewillfindithaslocalsuperlinearconvergencemteundersomereasonableconditionsInchapter3，Weproposes

8、affineinexactNewtonmethodwithprojectionandaffinescalinginteriormethodforsolvingboundconstrainedsemismoothequations11leaffinescalinginteriormethodisacombinationofinexactNewtOnmethodandlinesearchme山odIftheiteratedirectiond

9、oesn’tsatisfyacceptablerules，wecangetnewstepwhichCandecleasethefunctionvaluebyusingbothlinesearchandinteriorpointbacktrackingtechniqueWewillgiveafullproofoftheglobalandlocalsuperlinearconvergenceresultsFurthermorenumeric

10、alresultsa∞giventOindicatethatthealgorithmisusefulandeffectiveinpracticeFinallyinchapter5，asummaryofthispaperismadeandresearchdirectionisproposedKeyWords：nonlinearequations；semismooth；boundconstrained；inexactNewtonmethod