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1、ConvexOptimizationConvexOptimizationStephenBoydDepartmentofElectricalEngineeringStanfordUniversityLievenVandenbergheElectricalEngineeringDepartmentUniversityofCalifornia,LosAngelespublishedbythepresssyndicateoftheuniversityofcambridgeThePittBuilding,TrumpingtonSt
2、reet,Cambridge,UnitedKingdomcambridgeuniversitypressTheEdinburghBuilding,Cambridge,CB22RU,UK40West20thStreet,NewYork,NY10011-4211,USA477WilliamstownRoad,PortMelbourne,VIC3207,AustraliaRuizdeAlarc¶on13,28014Madrid,SpainDockHouse,TheWaterfront,CapeTown8001,SouthAfr
3、icahttp://www.cambridge.org°cCambridgeUniversityPress2004Thisbookisincopyright.Subjecttostatutoryexceptionandtotheprovisionsofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpubli
4、shed2004PrintedintheUnitedKingdomattheUniversityPress,CambridgeTypesetinComputerModernRomanusingLATEXAcataloguerecordforthisbookisavailablefromtheBritishLibraryLibraryofCongressCataloguinginPublicationdatanotyetavailableISBN0521833787hardbackForAnna,Nicholas,andN
5、oraDaniÄelandMargrietContentsPrefacexi1Introduction11.1Mathematicaloptimization........................11.2Least-squaresandlinearprogramming..................41.3Convexoptimization............................71.4Nonlinearoptimization..........................91.5
6、Outline...................................111.6Notation..................................14Bibliography...................................16ITheory192Convexsets212.1A±neandconvexsets...........................212.2Someimportantexamples.........................272
7、.3Operationsthatpreserveconvexity....................352.4Generalizedinequalities..........................432.5Separatingandsupportinghyperplanes..................462.6Dualconesandgeneralizedinequalities..................51Bibliography...........................
8、........59Exercises.....................................603Convexfunctions673.1Basicpropertiesandexamples......................673.2Operationsthatpreserveconve
