Nonsmooth analysis refers to differential analysis in the absence of differentiability. It can be regarded as a subfield of that vast subject known as nonlinear analysis. While nonsmooth analysis has classical roots （we claim to have traced its lineage hack to Dini）， it is only in the last decades that the subject has grown rapidly. To the point， in fact， that further development has sometimes appeared in danger of being stymied， due to the plethora of definitions and unclearly related theories.
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