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1、ConvexOptimizationConvexOptimizationStephenBoydDepartmentofElectricalEngineeringStanfordUniversityLievenVandenbergheElectricalEngineeringDepartmentUniversityofCalifornia,LosAngelescambridgeuniversitypressCambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,S˜aoPaolo,DelhiCambridgeUniversity
2、PressTheEdinburghBuilding,Cambridge,CB28RU,UKPublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYorkhttp://www.cambridge.orgInformationonthistitle:www.cambridge.org/9780521833783cCambridgeUniversityPress2004Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisi
3、onsofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublished2004Seventhprintingwithcorrections2009PrintedintheUnitedKingdomattheUniversityPress,CambridgeAcataloguerecordforthispublicationisavailablefromtheB
4、ritishLibraryLibraryofCongressCataloguing-in-PublicationdataBoyd,StephenP.ConvexOptimization/StephenBoyd&LievenVandenberghep.cm.Includesbibliographicalreferencesandindex.ISBN05218337871.Mathematicaloptimization.2.Convexfunctions.I.Vandenberghe,Lieven.II.Title.QA402.5.B692004519.6–dc222003063
5、284ISBN978-0-521-83378-3hardbackCambridgeUniversityPresshasnoresponsiblityforthepersistencyoraccuracyofURLsforexternalorthird-partyinternetwebsitesreferredtointhispublication,anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate.ForAnna,Nicholas,andNoraDani¨ela
6、ndMargrietContentsPrefacexi1Introduction11.1Mathematicaloptimization........................11.2Least-squaresandlinearprogramming..................41.3Convexoptimization............................71.4Nonlinearoptimization..........................91.5Outline.................................
7、..111.6Notation..................................14Bibliography...................................16ITheory192Convexsets212.1Affineandconvexsets...........................212.2Someimportantexamples.........................272.3Operationsthatpreservec
