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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.ThispageintentionallyleftblankPrefacePardonmeforwritingsuc
2、halongletter;Ihadnotthetimetowriteashortone.—LordChesterfieldNonsmoothanalysisreferstodifferentialanalysisintheabsenceofdiffer-entiability.Itcanberegardedasasubfieldofthatvastsubjectknownasnonlinearanalysis.Whilenonsmoothanalysishasclassicalroots(weclaimtohavetraceditslineagebacktoDini),itisonlyint
3、helastdecadesthatthesubjecthasgrownrapidly.Tothepoint,infact,thatfurtherdevel-opmenthassometimesappearedindangerofbeingstymied,duetotheplethoraofdefinitionsandunclearlyrelatedtheories.Onereasonforthegrowthofthesubjecthasbeen,withoutadoubt,therecognitionthatnondifferentiablephenomenaaremorewidespr
4、ead,andplayamoreimportantrole,thanhadbeenthought.Philosophicallyatleast,thisisinkeepingwiththecomingtotheforeofseveralothertypesofirregularandnonlinearbehavior:catastrophes,fractals,andchaos.Inrecentyears,nonsmoothanalysishascometoplayaroleinfunctionalanalysis,optimization,optimaldesign,mechani
5、csandplasticity,differen-tialequations(asinthetheoryofviscositysolutions),controltheory,and,increasingly,inanalysisgenerally(criticalpointtheory,inequalities,fixedpointtheory,variationalmethods...).Inthelongrun,weexpectitsmeth-odsandbasicconstructstobeviewedasanaturalpartofdifferentialanalysis.vii
6、iPrefaceWehavefoundthatitwouldberelativelyeasytowriteaverylongbookonnonsmoothanalysisanditsapplications;severaltimes,wedid.Wehavenowmanagednottodoso,andinfactourprincipalclaimforthisworkisthatitpresentstheessentialsofthesubjectclearlyandsuccinctly,togetherwithsomeofitsapplicationsandageneroussu
7、pplyofinterestingexercises.Wehavealsoincorporatedinthetextanumberofnewresultswhichclarifytherelationshipsbetweenthedifferentschoolsofthoughtinthesubject.Wehopethatthiswillhelpmakenonsmoothanalysisaccessibletoawideraudience.Inthissp
