文档介绍：MINICOURSENOTESbasedon
OONVEXANALYSISANDNONLINEAR
OPTIMIZATION
SpringerVerlag,inpIeSS
1
0
TMRorw
CeutreforExberineutalandCoustructiveMathematics
DeparumentefMathematiesandStalisties
anadaV5A186
and
DeparumentofCombinateriesandOptiunivation
UmiversityofWaterlooWarerloo,Ont,CanadaK2f3G1
aslew
Giorionmgaterlooca
April51999
alyopporedhyeNomlsinneondFngioeeneHeerhdoue
Contents
0Pnefoee
1Backgrouna
1Eneliiomspaees
12Spuametieamtricee,
2Tequalityconstraints
21Opinaliconditions。
22Iheorneoflletenutiwe
23Msefuetiotsandfistorlercomditots
3Fenchelduality
91Subeadieatsandeouvexfiaetions
932Uheueuaetion
33Thefeacheleorjugnte。
4Convexanalysis
4lContidityofeouexfanetiong.、
42feuetelbioonjagation.。
13Lngnagiondulity
5Specialcases
Polyledraleovesetsaudfiaetiong
Fuuetionsfdigomales
Dualityforlineurndsonidetiite
Ing
5Conmexoce
88
8
s
00
05
102
TheVariationaPrindipleLa
6bcintoductiontoumetcngdortty吴
xedpoints19
2Dnouserseedpoate
72Solectiouesdltsudtheultaaifuafedpobttieoren,26
73Wariutomliegltt133
Optimizationisaichandthrivingmathematicaldisct
Dline,Propertiesofminimizersandmaximizersoffunc
tiongrelyintimatelyonawealthoftechniqhtesfrommath
ematicalanalysisincludingtoolsfromcalcuusandits
8eneralizationg,topologicalnotiong,andmoregeomet
ricidens,Thetheoryunderlyingcurrentcomputational
optimiyationtcchnidticsgrowscvermorcgophisticated一
dualitybasedalgorithmsandinteriorpointmethodsare
tyDicalexamples,ThepowerfulandclegantIanguageof
convexanalysisunifesmuchfth识theory,Henceour
aimofWiting8concise,aceessibleacconntafconvex
analysisanditsapplication8andextensions,forabroad
audience.
Forstudentsofoptimizationandanalysisthereisgreat
benefittobltmingthedistinctionbetweenhetwodis
ciplines,Manyimportantanalyticproblemshayeilumi
natingoptimizationformulationsandhencecanbeap
ProachedthroughourmainvariationaltoolsSubgradi
entsandoptimalityconditiongthemanyguisesofdual
itymetricregulanityand8oIorth,Moregenerally,the
ideaofconvexity识cen