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ID:34860814
大小:1.25 MB
页数:261页
时间:2019-03-12
《Springer.Auslender,Teboulle(2003).Asymptotic.Cones.and.Functions.in.Optimization.and.Variational.Inequalities.(Springer)》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、AsymptoticConesandFunctionsinOptimizationandVariationalInequalitiesAlfredAuslenderMarcTeboulleSpringerThisbookisdedicatedtoMartine,Fran¸cois,andJ´erˆomeRachel,Yoav,Yael,andKerenThispageintentionallyleftblankPrefaceNonlinearappliedanalysisandinparticulartherelatedfieldsofcontinuousoptimiza
2、tionandvariationalinequalityproblemshavegonethroughmajordevelopmentsoverthelastthreedecadesandhavereachedmaturity.Apivotalroleinthesedevelopmentshasbeenplayedbyconvexanalysis,arichareacoveringabroadrangeofproblemsinmathematicalsciencesanditsapplications.SeparationofconvexsetsandtheLegend
3、re–Fenchelconjugatetransformsarefundamentalnotionsthathavelaidthegroundforthesefruitfuldevelopments.Twootherfundamentalnotionsthathavecontributedtomakingconvexanalysisapowerfulanalyticaltoolandthathaveoftenbeenhiddeninthesedevelopmentsarethenotionsofasymptoticsetsandfunctions.Thepurposeo
4、fthisbookistoprovideasystematicandcomprehensiveaccountofasymptoticsetsandfunctions,fromwhichabroadanduse-fultheoryemergesintheareasofoptimizationandvariationalinequali-ties.Thereisavarietyofmotivationsthatledmathematicianstostudyquestionsrevolvingaroundattaintmentoftheinfimuminaminimizati
5、onproblemanditsstability,dualityandminmaxtheorems,convexificationofsetsandfunctions,andmaximalmonotonemaps.Inallthesetopicswearefacedwiththecentralproblemofhandlingunboundedsituations.Thisisparticularlytruewhenstandardcompactnesshypothesesarenotpresent.Theappropriateconceptsandtoolsneeded
6、tostudysuchkindsofproblemsarevitalnotonlyintheorybutalsowithinthedevelopmentofnumericalmethods.Forthelatter,weneednotonlytoprovethatase-quencegeneratedbyagivenalgorithmiswelldefined,namelyanexistenceviiiresult,butalsotoestablishthattheproducedsequenceremainsbounded.Onecanseldomdirectlyapp
7、lytheoremsofclassicalanalysistoanswertosuchquestions.Thenotionsofasymptoticconesandassociatedasymp-toticfunctionsprovideanaturalandunifyingframeworktoresolvethesetypesofproblems.Thesenotionshavebeenusedmostlyandtraditionallyinconvexanalysis,withmanyresultsscatteredintheli
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