Abstract
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 [15] in early 70’s (and called H-convexity there) and the definition of what is now called “viscosity subdifferentials”, which first appeared in [7] some ten years later, is easily detectable.
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Ioffe, A.D. (2001). Abstract convexity and non-smooth analysis. In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 3. Springer, Tokyo. https://doi.org/10.1007/978-4-431-67891-5_2
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DOI: https://doi.org/10.1007/978-4-431-67891-5_2
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