From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules
We derive exact calculus rules for the directed subdifferential defined for the class of directed subdifferentiable functions. We also state optimality conditions, a chain rule and a mean-value theorem. Thus, we extend the theory of the directed subdifferential from quasidifferentiable to directed subdifferentiable functions.
KeywordsNonconvex subdifferentials Directional derivatives Difference of convex (DC) functions Mean-value theorem and chain rule for nonsmooth functions
Mathematics Subject Classification49J52 90C26 26B25 58C20
We thank Wolfgang Achtziger for motivating us to study the mean-value theorem. This work was partially supported by The Hermann Minkowski Center for Geometry at Tel Aviv University, Tel Aviv, Israel.
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