Nearly convex sets: fine properties and domains or ranges of subdifferentials of convex functions

Published 25 Jul 2015 in math.OC | (1507.07145v1)

Abstract: Nearly convex sets play important roles in convex analysis, optimization and theory of monotone operators. We give a systematic study of nearly convex sets, and construct examples of subdifferentials of lower semicontinuous convex functions whose domain or ranges are nonconvex.

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