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1、Vector-ValuedOptimizationProblemsinControlTheoryACADEMICPRESSRAPIDMANUSCRIPTREPRODUCTIONThisisVolume148inMATHEMATICSINSCIENCEANDENGINEERINGASeriesofMonographsandTextbooksEditedbyRICHARDBELLMAN,UniversityofSouthernCaliforniaThecompletelistingofbooksinthisseriesisavailablefromthePubl
2、isheruponrequest.VECTOR-VALDEDOPTIMIZATIONPROBLEMSINCONTROLTHEORYM.E.SALUKVADZECONTROLSYSTEMSINSTITUTESOVIETGEORGIATRILISI.U.S.S.R.TranslatedByJOHNL.CASTlDEPARTMENTOFCOMPUTERAPPLICATIONSANDINFORMATIONSYSTEMSNEWYORKUNIVERSITYNEWYORK,NEWYORKACADEMICPRESSASubsidiaryofHarcourtBraceJova
3、novich,PublishersNewYorkLondonTorontoSydneySanFrancisco1979COPYRIGHT?1979,BYACADEMICPRESS,INC.ALLRIGHTSRESERVED.NOPARTOFTHISPUBLICATIONMAYBEREPRODUCEDORTRANSMIfTEDINANYFORMORBYANYMEANS,ELECTRONICORMECHANICAL,INCLUDINGPHOTOCOPY,RECORDING,ORANYINFORMATIONSTORAGEANDRETRIEVALSYSTEM,WIT
4、HOUTPERMISSIONINWRITINGFROMTHEPUBLISHER.ACADEMICPRESS,INC.111FifthAvenue.NewYork,NewYork10003UnitedKingdomEditionpublishedbyACADEMICPRESS,INC.(LONDON)LTD.24/28OvalRoad,LondonNWI7DXLibraryofCongressCataloginginPublicationDataSalukvadze,MindiiaEvgen'evich,Vector-valuedoptimizationpro
5、blemsincontroltheory.(MathematicsinScienceandEngineering;148)TranslationofZadachivektornoioptimizaisiivieoriiupravleniia.I.Controltheory.2.Automaticcontrol.3.Mathematicaloptimization.4.Vectorvaluedfunctions.I.Title.II.Series.QA402.3.S24613629.8'31279-23364ISBN0-12-616750-8Originall
6、ypublishedintheU.S.S.R.underthetitleZadachivektornoioptimizatsiivteoriiupravlenia,MetsnierebaPublishingHouse,1975PRINTEDINTHEUNITEDSTATESOFAMERICA79808182987654321ContentsIntroductionviiChapter1ASurveyofOptimizationProblemswithVectorCriteria1.1GeneralSurveyoftheProblemI1.2TheRemark
7、sofL.A.Zadeh101.3OptimizationofanOrderedSetofScalarCriteriaII1.4HierarchicalRankingofScalarCriteria171.5UnimprovableSolutionsintheProblemofVectorOptimization(ParetoOptimality)191.6TheWorkofA.SalammaandV.Gourishankar231.7SolutionsinFuzzyNeighborhoods25Chapter2TheFormulationofOptimiz
8、ationProblemswithVectorFun
