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In this paper, we revisit the Mordukhovich's subdifferential criterion forLipschitz continuity of nonsmooth functions and coderivative criterion for theAubin/Lipschitz-like property of set-valued mappings in finite dimensions. Thecriteria are useful and beautiful results in modern variational analysisshowing the state of the art of the field. As an application, we establishnecessary and sufficient conditions for Lipschitz continuity of the minimaltime function and the scalarization function, that play an important role inmany aspects of nonsmooth analysis and optimization.

Lipschitz Properties of Nonsmooth Functions and Set-Valued Mappings via Generalized Differentiation and Applications