Mean value theorems in nonsmooth analysis
J.-B. Hiriart-Urruty · Numerical Functional Analysis and Optimization · 1980
Different extensions of the notion of gradient in differentiable analysis and of subdifferential in convex analysis are used in order to derive mean value theorems for non-differentiable functions. Previous results dealing with convex or locally Lipschitz real-valued functions are extended. In addition, mean value theorems in an equality form are described for locally Lipschitz vector-valued mappings.