Matlab---Optimisation-Toolbox---Users-Guide

ComputationVisualizationProgrammingForUsewithMATLAB®User’sGuideVersion2OptimizationToolboxHowtoContactTheMathWorks:@[e-mail][e-mail]@[e-mail],licenserenewals,[e-mail],pricing,andgeneralinformation508-647-7000Phone[phone]FaxTheMathWorks,Inc.Mail3AppleHillDriveNatick,MA01760-2098Forcontactinformationaboutworldwideoffices,seetheMathWorksWebsite.OptimizationToolboxUser’sGuideCOPYRIGHT1990-2002byTheMathWorks,Inc.Thesoftwaredescribedinthisdocumentisfurnishedunderalicenseagreement.Thesoftwaremaybeusedorcopiedonlyunderthetermsofthelicenseagreement.Nopartofthismanualmaybephotocopiedorrepro-ducedinanyformwithoutpriorwrittenconsentfromTheMathWorks,Inc.FEDERALACQUISITION:ThisprovisionappliestoallacquisitionsoftheProgramandDocumentationbyorforthefederalgovernmentoftheUnitedStates.ByacceptingdeliveryoftheProgram,thegovernmentherebyagreesthatthissoftwarequalifiesascommercialcomputersoftwarewithinthemeaningofFARPart12.212,DFARSPart227.7202-1,DFARSPart227.7202-3,DFARSPart252.227-7013,andDFARSPart252.227-7014.ThetermsandconditionsofTheMathWorks,Inc.SoftwareLicenseAgreementshallpertaintothegovernment’suseanddisclosureoftheProgramandDocumentation,andshallsupersedeanyconflictingcontractualtermsorconditions.Ifthislicensefailstomeetthegovernment’sminimumneedsorisinconsistentinanyrespectwithfederalprocurementlaw,thegovernmentagreestoreturntheProgramandDocumentation,unused,toMathWorks.MATLAB,Simulink,Stateflow,HandleGraphics,andReal-TimeWorkshopareregisteredtrademarks,andTargetBoxisatrademarkofTheMathWorks,Inc.Otherproductorbrandnamesaretrademarksorregisteredtrademarksoftheirrespectiveholders.PrintingHistory:November1990FirstprintingDecember1996SecondprintingForMATLAB5January1999ThirdprintingForVersion2(Release11)September2000FourthprintingForVersion2.1(Release12)June2001OnlineonlyRevisedforVersion2.1.1(Release12.1)July2002OnlineonlyRevisedforVersion2.2(Release13)iContentsPrefaceUsingThisGuide.....................................viiiRelatedProducts......................................ixTypographicalConventions............................xi1IntroductionWhatIstheOptimizationToolbox?.....................1-2NewFeaturesinVersion2.2...........................1-3NewfsolveDefaultAlgorithm..........................1-3ConfigurationInformation............................1-4TechnicalConventions................................1-5Matrix,Vector,andScalarNotation.....................1-5Acknowledgments....................................1-62TutorialIntroduction.........................................2-3ProblemsCoveredbytheToolbox........................2-3UsingtheOptimizationFunctions.......................2-5iiContentsExamplesthatUseStandardAlgorithms................2-7UnconstrainedMinimizationExample....................2-8NonlinearInequalityConstrainedExample...............2-9ConstrainedExamplewithBounds.....................2-11ConstrainedExamplewithGradients...................2-12GradientCheck:AnalyticVersusNumeric...............2-14EqualityConstrainedExample.........................2-15Maximization.......................................2-16Greater-Than-ZeroConstraints........................2-16AdditionalArguments:AvoidingGlobalVariables.........2-16NonlinearEquationswithAnalyticJacobian..............2-17NonlinearEquationswithFinite-DifferenceJacobian......2-20MultiobjectiveExamples..............................2-21Large-ScaleExamples................................2-33ProblemsCoveredbyLarge-ScaleMethods...............2-34NonlinearEquationswithJacobian.....................2-37NonlinearEquationswithJacobianSparsityPattern.......2-39NonlinearLeast-SquareswithFullJacobianSparsityPattern............................................2-41NonlinearMinimizationwithGradientandHessian.......2-43NonlinearMinimizationwithGradientandHessianSparsityPattern............................................2-44NonlinearMinimizationwithBoundConstraintsandBandedPreconditioner......................................2-46NonlinearMinimizationwithEqualityConstraints........2-50NonlinearMinimizationwithaDensebutStructuredHessianandEqualityConstraints.............................2-51QuadraticMinimizationwithBoundConstraints..........2-55QuadraticMinimizationwithaDensebutStructuredHessian............................................2-57LinearLeast-SquareswithBoundConstraints............2-60LinearProgrammingwithEqualitiesandInequalities......2-61LinearProgrammingwithDenseColumnsintheEqualities.2-62DefaultParameterSettings...........................2-65ChangingtheDefaultSettings.........................2-65DisplayingIterativeOutput...........................2-68OutputHeadings:Medium-ScaleAlgorithms.............2-68iiiOutputHeadings:Large-ScaleAlgorithms...............2-71OptimizationofInlineObjectsInsteadofM-Files.......2-74TypicalProblemsand