解無(wú)約束優(yōu)化的漸弱過(guò)濾集方法.pdf

1、南京師范大學(xué)碩士學(xué)位論文解無(wú)約束優(yōu)化的漸弱過(guò)濾集方法姓名：陳艷男申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：孫文瑜20070101AbstractManyimportantproblemsc3nbeexpressedinterui8ofnonconvexnonfinearmultivariateunconstrainedoptimizationproblemsTwobroadclassesofMgorithmsfortheunconstr

2、ainedoptimizationproblenm口elinesearchalgorittnnsandtrust—re；ioilalgorithmsSincefiltertocJmiqucwasintrodu(『cdbyFletcherandLeyffcrin1997midsubsequentlypublishedas【131filtertechniquehasbeenstudiedandappliedinmanyareas，andit

3、performswellWeproposedanewdwindlingfiltertechniqueforlargescaleunconstrainedoptimizationproblemsGenerally：forthepurposeofgiobalconvergeltce，themultidimensionalfilterf21，25，271iscoveredbyafixedenvelopeSinceafixedenvelopei

4、snotsuitableforbacktrackinglinesearchprocess，wefurtherstudyitinthisthesisandputforwardaconceptionofdwindlingfiltertechniqueThemainideaisthatthedwindlingfilterenvelopeisnotfixed，butbecomesthinnerandthinnerasthesteplengtho

5、fthebacktrackingfinesearchbecomessmallerandsmallerNaturally，combinationofthedwindlingfiltertechliiqueandthesecond—orderlinesearchmethodisaverysignificantalgorithmforunconstrainedoptimizationThenewalgorithmisshowntobeglob

6、allyconvergentt0onesecondorderstationarypointatleastPreliminarynumericalexperimentsonasetofCUTErtestproblemsindicatethatthenewalgorithmisverycompetitivewithsolneclassicallinesearchalgorithmsWeshowthatthelinkedlistconstru

7、ctionintheFORTRANlanguageworkswellaaldthatthestorageofthedwindlingfiIterismediumAndthen，wenoticethatthetrtLstregionmethodisahvaysmoreeffectivethanlinesearchmethodThisinspke118toapplythedwindlingfiltertechniqueintrustre西O

8、nlinesearchframeworktogiveanothernewalgorithmWeprovethatunderreasonableMSUlllp—tionsthenewalgorithmconvergestoonesecondorderstationarypointatleastSomepreliminarynumericalresultsOilasetofCUTErtestproblemsarereportedwhichs