Nonsmoothanalysisreferstodifferentialanalysisintheabsenceofdifferentiability.Itcanberegardedasasubfieldofthatvastsubjectknownasnonlinearanalysis.Whilenonsmoothanalysishasclassicalroots(weclaimtohavetraceditslineagehacktoDini),itisonlyinthelastdecadesthatthesubjecthasgrownrapidly.Tothepoint,infact,thatfurtherdevelopmenthassometimesappearedindangerofbeingstymied,duetotheplethoraofdefinitionsandunclearlyrelatedtheories.