We show that the directed subdifferential introduced for differences of convex (delta-convex, DC) functions by Baier and Farkhi can be constructed from the directional derivative without using any information on the delta-convex structure of the function. The new definition extends to a more general class of functions, which includes Lipschitz functions definable on o-minimal structure and quasidifferentiable functions.
- Difference of convex (delta-convex, DC) functions
- Differences of sets
- Directional derivatives
- Nonconvex subdifferentials