一類求解非線性互補(bǔ)問題的廣義Newton算法.pdf

1、南京航空航天大學(xué)碩士學(xué)位論文一類求解非線性互補(bǔ)問題的廣義Newton算法姓名：閔嬌申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：運(yùn)籌學(xué)與控制論指導(dǎo)教師：殷洪友20080201一類求解非線性互補(bǔ)問題的廣義Newton算法iiAbstractThenonlinearcomplementarityproblemisaveryimptantpartinmathematicalprogramming.Ithasbeenwidelyusedinthefieldofeco

2、nomicsengineer.Theresearchonitisalwaysahottopicinnonlinearcomputationalscience.goodachievementshavegotatthestudyofthealgithmsinsolvingcomplementarityproblems.Thispapermainlystudiedsnonsmoothcomplementarityproblem.Afterst

3、udyingallkindsofalgithmssemismooththeieswestudiesthesmoothNewtonalgithmfurtherly.Throughthestudyofmanycomplementarityfunctionswecouldfindthatsomeofthemaresilimarinshape.Firstlyweadvanceakindofnewcomplementarityfunction.T

4、hisfunctionincludefamousFisherfunctiontheminimalfunction.Accdingtothisfunctionwecanconvertsolvingthecomplementarityproblemtosolvingthenonlinearequations.Howeverthisfunctionisnotdifferentialattheacnodestheequationswehaveg

5、otarenonsmooth.Becauseofthequestionsabovewestructasmoothapproachofthefmerfunction.AfterconvertingthenonsmoothequationstothesmoothonesweusethegeneralizedsmoothNewtonmethodtosolvethem.Weprovethatthealgithmhadglobalconverge

6、ncelocalconvergence.Numericalexperimentsshowthatthealgithmhasgoodeffectsinsolvingthecomplementarityproblems.Howeverwhenthederivativematrixissingularthisalgithmlostefficacy.Soonthebaseofthefirstalgithmweadvanceanotheronew

7、hichhasn’tanyneedfthederivativematrix.Choosingsomeproperparametersweproveitsglobalconvergence.Numericalexperimentsalsomakethegoodpropertiesofthisalgithmclear.Keywds:complementarityproblem，semismooth，equations，Newtonalgit