2056.有限多個(gè)變分不等式的一般迭代法及在優(yōu)化中的應(yīng)用

1、學(xué)校代碼：10270分類號(hào)：0177學(xué)號(hào)：142200638上善_說大爹碩士學(xué)位論文有限多個(gè)變分不等式的一般迭代法及在優(yōu)化中的應(yīng)用學(xué)院：_______數(shù)理學(xué)院專業(yè)：運(yùn)籌學(xué)與控制論研究方向：:變分不等式與算算子逼近研究生姓名宋月指導(dǎo)教師：曾六:川完成日期2017年3月15日Title:GeneralIterativeMethodsfFinitelyManyVariationalInequalitieswithApplicationstoO

2、ptimizationProblemsMaj:OperationsResearchControlTheyDegreeApplicant:YueSongTut:LiuchuanZengProfessAbstractInthispaperweintroduceageneraliterativemethodfacertainoptimizationproblemofwhichtheconstrainedsetistheintersection

3、alsetofthesolutionsetoffinitelymanyvariationalinequalityproblemsfcontinuousmonotonemappingsthesolutionsetoffinitelymanyvariationalinclusionproblemsandthefixedpointsetofacontinuouspseudocontractivemappinginarealHilbertspa

4、ce.Thispaperconsistsoffourchapters.Nowwedescribethemonebyone.InChapter1werecallthesimplehistyofthevariationalinequalitytheyandstatethemainwkofthispaper.InChapter2weintroducetheimplicititerativealgithmanditsproperties.InC

5、hapter3undersomesuitablecontrolconditionsaccdingtothepropertiesoftheimplicititerativemethodweestablishthestrongconvergenceoftheproposedmethodtoanelementoftheintersectionalsetwhichistheuniquesolutionofacertainoptimization

6、problem.Asadirectconsequenceweobtaintheuniqueminimumnmelementoftheintersectionalset.InChapter4weintroduceanexplicititerativemethodandalsomaketheconvergenceanalysisoftheexplicititerativemethodinthesameway.Theresultspresen

7、tedinthispaperimproveextendanddevelopsomerecentcrespondingresultsintheliterature.KeyWds:GeneraliterativemethodOptimizationproblemContinuousmonotonemappingContinuouspseudocontractivemappingInversestronglymonotonemappingNo