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1、NonsmoothAnalysisandControlTheoryF.H.Clarke,etal.Springer1.ControlTheory.2.Nonsmoothoptimization.I.Clarke,FrancisH.II.Series.Theauthorsdedicatethisbook:toGail,Julia,andDanielle;toSofia,Simeon,andIrina;toJudy,Adam,andSach;andtoMaryandAnna.Thispageinten
2、tionallyleftblankPrefacePardonmeforwritingsuchalongletter;Ihadnotthetimetowriteashortone.—LordChesterfieldNonsmoothanalysisreferstodifferentialanalysisintheabsenceofdiffer-entiability.Itcanberegardedasasubfieldofthatvastsubjectknownasnonlinearanalysis.Wh
3、ilenonsmoothanalysishasclassicalroots(weclaimtohavetraceditslineagebacktoDini),itisonlyinthelastdecadesthatthesubjecthasgrownrapidly.Tothepoint,infact,thatfurtherdevel-opmenthassometimesappearedindangerofbeingstymied,duetotheplethoraofdefinitionsandun
4、clearlyrelatedtheories.Onereasonforthegrowthofthesubjecthasbeen,withoutadoubt,therecognitionthatnondifferentiablephenomenaaremorewidespread,andplayamoreimportantrole,thanhadbeenthought.Philosophicallyatleast,thisisinkeepingwiththecomingtotheforeofseve
5、ralothertypesofirregularandnonlinearbehavior:catastrophes,fractals,andchaos.Inrecentyears,nonsmoothanalysishascometoplayaroleinfunctionalanalysis,optimization,optimaldesign,mechanicsandplasticity,differen-tialequations(asinthetheoryofviscositysolution
6、s),controltheory,and,increasingly,inanalysisgenerally(criticalpointtheory,inequalities,fixedpointtheory,variationalmethods...).Inthelongrun,weexpectitsmeth-odsandbasicconstructstobeviewedasanaturalpartofdifferentialanalysis.viiiPrefaceWehavefoundthatit
7、wouldberelativelyeasytowriteaverylongbookonnonsmoothanalysisanditsapplications;severaltimes,wedid.Wehavenowmanagednottodoso,andinfactourprincipalclaimforthisworkisthatitpresentstheessentialsofthesubjectclearlyandsuccinctly,togetherwithsomeofitsapplic
8、ationsandageneroussupplyofinterestingexercises.Wehavealsoincorporatedinthetextanumberofnewresultswhichclarifytherelationshipsbetweenthedifferentschoolsofthoughtinthesubject.Wehopethatthiswillhelpmakenonsmoothanalysisaccessibletoawideraudience.Inthissp
