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1、IntroductiontotheTheoryofNonhnearOptimizationJohannesJahnIntroductiontotheTheoryofNonHnearOptimizationThirdEditionWith31FiguresSpringerProf.Dr.JohannesJahnUniversitatErlangen-NiirnbergInstitutfurAngewandteMathematikMartensstr.391058ErlangenGermanyjahn@am.uni-erlangen.deLibraryofCo
2、ngressControlNumber:2006938674ISBN978-3-540-49378-5SpringerBerlinHeidelbergNewYorkISBN978-3-540-61407-4SecondEditionSpringerBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,rep
3、rinting,reuseofillustrations,recitation,broad?casting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysb
4、eobtainedfromSpringer.ViolationsareliabletoprosecutionundertheGermanCopyrightLaw.SpringerispartofSpringerScience+BusinessMediaspringer.com?Springer-VerlagBerlinHeidelberg1994,1996,2007Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,even
5、intheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Production:LE-TgXJelonek,Schmidt&VocklerGbR,LeipzigCover-design:ErichKirchner,HeidelbergSPIN1193204842/3100YL-543210Printedonacid-freepaperToClaudiaandMa
6、rtinPrefaceThisbookpresentsanapplication-orientedintroductiontothethe?oryofnonhnearoptimization.Itdescribesbasicnotionsandconcep?tionsofoptimizationinthesettingofnormedorevenBanachspaces.VarioustheoremsareappHedtoproblemsinrelatedmathematicalareas.Forinstance,theEuler-Lagrangeequa
7、tioninthecalculusofvariations,thegenerahzedKolmogorovconditionandthealternationtheoreminapproximationtheoryaswellasthePontryaginmaximumprincipleinoptimalcontroltheoryarederivedfromgeneralresultsofoptimization.Becauseoftheintroductorycharacterofthistextitisnotintendedtogiveacomplet
8、edescriptionofallapproachesinopti
