一些新的非線(xiàn)性共軛梯度法.pdf

1、湘潭大學(xué)碩士學(xué)位論文一些新的非線(xiàn)性共軛梯度法姓名：周光明申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：袁亞湘成央金20030401ABSTRACTThispaperconsistsoffourchaptersInthefirstchapter，wesimplyrevieworigin，developmentandcharacteristicsofnontnearconjugategradientmethodforsolvingunconst

2、rainedoptimization，introducesomeimportantformulasofthemethodNonlinearCOnjugategradientmethodisaveryimportantmethodbecauseithasadvantagesthatitsalgorithmisverysimpleanditdoesnotrequirethestorageofanymatricesItisverysuited

3、tosolvingsomelargescaleproblemsInchapter2，weproposeanewformulaofmainparameter盧女ofconjugategradientmethodthatisrelatedtodecreaseofobjectivefunction，testitsnumericaleffedsandanalyzeitsconvergentpropertiesByrestrictingthene

4、wformula廈tononnegativedomains，weconstructtwohybridformulasanddiscusstheirconvergentpropertiesundersomeweakconditionsTheirnumericalresultsshowthattheyareefficientandrobustTheireffectsareinsomeextentbetterthanPRP。SoneIncha

5、pter3，byminimizingaquadraticmodelrestrictingnextsearchdirectiontoasubsetofSpangI，d“，weproposeotherformulaofparameter成Convergencesofthenewmethodanditshybridformulaareprovedundermonotone1inesearchTheirnumericalresultsshowt

6、hattheyareefficientBasedontheP印ers『101and【19]，weproposeaNewnonmonotoneCOnjugategradientalgorithm，proveitsconvergenceandtestthenewnonmonotonealgorihmInthelastchapter，wemakefurtherdiscussiononconjugategradientmethodFirstly

7、，weintroducetwogeneralizedconjugategradientmethodsSomeoftheexistingproblemsonconjugategradientarepresentedinthelastsectionKeyWords：unconstrainedoptimization，nonlinearconjugategradientmethod，linesearch，convergence，numeric