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1、内蒙古工业大学硕士学位论文II内蒙古工业大学硕士学位论文AbstractVariationalinequalityproblem(VIP)isabasicprobleminoperationalresearch,atthesametime,economics,ecology,engineeringscienceandfinanceandmanyfieldshaveawiderangeofapplications.Therefore,sincethe1960s,thevariationalinequalityproblemespeciallyitsnumericalcalculationmet
2、hodhasreceivedwideattentionofmanyresearchers.SuchassomeknownmethodsincludingNewtonmethod,alternatingdirectionsmethod,nearpointmethodandinterior-pointmethod,neuralnetworkandprojectionmethods,amongthem,theprojectionandcontractionmethodwiththecharacteristicsofsimpleeasytooperate,butalsogotthefavourofm
3、anyscholars.Alltheseresearchesemergeendlessly,theProjectionandContractionMethodputforwardbyBingshengHeisoneofthecategory.Thecharacteristicofprojectionandcontractionmethodisthateachiterationcomputationaregenerallysimplecalculationofsomefunctionstothefeasiblesetofprojection.Andthemainideaofthisarticl
4、eistocarryonthedeepresearchandattempttoconstructanewprojectionandcontractionmethodtosolvethevariationalinequalityproblems.Specificworkistoimprovetheexistingprojectionandcontractionmethod.BytheexplorationonthesearchdirectionofBingshengHestudytoconsidertheselectionofstep.Bythepremiseoffallingintheori
5、ginaldirection,togetaefficientstep-size.Findanewprojectionandcontractionmethodtosolvethevariationalinequalityproblem.Thecontent:Thefirstchapterismainlytheintroduction.Firstofall,carryonthesimpleintroductionoftheemergenceofthevariationalinequalityproblem,development,andotherbackgroundknowledge.Nextp
6、resentsbasicconceptsandconclusionofavariationalinequalityproblemandtheprojectionontheconvexset.Then,introducesseveralcommonmethodsforsolvingvariationalinequalityproblems.Finally,givethearrangementofthecontentattheendofthischapterinthispaper.III内蒙古工业大学硕士学位论文Thesecondchapterfirstlygivessomeinequaliti
7、esaboutvariationalinequalityproblemandthebasicideaoftheprojectionandcontractionmethodsproposedbyBingshengHefromtheNanJingUniversity.Secondly,combiningwiththepaperofmyseniorJinlongWang,analysisthemechanismof
