Abstract convexity and non-smooth analysis
Extensions of the concept of (convex) subdifferentials to models of so-called abstract convexity are well known and actually simple and natural (see e.g. [15, 16, 18, 19]). However it seems that very few basic facts of convex sub-differential calculus have been actually extended to the abstract convexity setting. Even less is known about interrelations between abstract convexity and nonconvex subdifferential theories, in spite of the fact that a similarity between the definition of subdifferential in the general model introduced in  in early 70’s (and called H-convexity there) and the definition of what is now called “viscosity subdifferentials”, which first appeared in  some ten years later, is easily detectable.
Mathematics Subject Classification (2000)49J52 90C48
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