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1、COMPUTATIONALMETHODSINOPTIMIZATIONAUnifiedApproachThisisVolume77inMATHEMATICSINSCIENCEANDENGINEERINGAseriesofmonographsandtextbooksEditedbyRICHARDBELLMAN,UniversityofSouthernCaliforniaAcompletelistofthebooksinthisseriesappearsattheendofthisvolume.COMPUTATIONALMETHODSINOPTIMIZATIONAUnifiedAppr
2、oachE.PolakDEPARTMENTOFELECTRICALENGINEERINGANDCOMPUTERSCIENCESUNIVERSITYOFCALIFORNIABERKELEY,CALIFORNIA1971ACADEMICPRESSNewYorkandLondonCOPYRIGHT01971,BYACADEMICPRESS,INC.ALLRIGHTSRESERVEDNOPARTOFTHISBOOKMAYBEREPRODUCEDINANYFORM,BYPHOTOSTAT,MICROFILM,RETRIEVALSYSTEM,ORANYOTHERMEANS,WITHOUTWR
3、ITTENPERMISSIONFROMTHEPUBLISHERS.REPRODUCTIONINWHOLEORINPARTFORANYPURPOSEOFTHEUNITEDSTATEGOVERNMENTISPERMITTED.ACADEMICPRESS,INC.111FifthAvenue,NewYork,NewYork10003UnitedKingdomEditionpublishedbyACADEMICPRESS,INC.(LONDON)LTD.BerkeleySquareHouse,LondonWlX6BALIBRARYOFCONGRESSCATALOGCARDNUMBER:7
4、2-134540AMS(M0S)1970SUBJECTCLASSIFICATIONS:90C30,90C50,49D05,49D10,49D15,49D30,49D35,49D40,49D45,49D99,34B05,34B15,34B99,3900,65H10,65K05,65L10,65Q05PRINTEDINTHEUNITEDSTATESOFAMERICATOORENANDSHARONThispageintentionallyleftblankPrefaceixNotetotheReaderxiiiConventionsandSymbolsxv1PRELlMINARYRES
5、ULTS11.1NonlinearProgrammingandOptimalControlProblems11.2OptimalityConditions71.3ModelsandConvergenceConditionsforComputationalMethods122UNCONSTRAlNEDMINIMIZATlON282.1GradientandQuasi-NewtonMethodsinRn282.2ReductionofDerivativeCalculations402.3ConjugateGradientMethodsin[Wn442.4UnconstrainedDi
6、screteOptimalControlProblems662.5UnconstrainedContinuousOptimalControlProblems713EQUALITYCONSTRAINTS:ROOTANDBOUNDARY-VALUEPROBLEMS793.1ZerosofaFunctionandProblemswithEqualityConstraintsinRn793.2Boundary-ValueProblemsandDiscreteOptimalControl833.3Boundary-ValueProblemsandContinuousOptimalContr
7、ol1034EQUALITYANDINEQUALITYCONSTRAINTS1264.1PenaltyFunctionMethods1264.2MethodsofCenters150viiviiiCONTENTS4.3MethodsofFeasibleDirections1594.4Second-OrderMethodsofFeasibleDirections1804.5GradientProjectionMethods1855CONVEXOPTIMALCONTROLPROBLE
