Abstract
It is well known that the subgradient mapping associated with a lower semicontinuous function is maximal monotone if and only if the function is convex, but what characterization can be given for the case in which a subgradient mapping is only maximal monotone locally instead of globally? That question is answered here in terms of a condition more subtle than local convexity. Applications are made to the tilt stability of a local minimum and to the local execution of the proximal point algorithm in optimization.
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