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

2015/07/25 by Moffat, Sarah M., Moursi, Walaa M., Wang, Xianfu
#26A51 #47H05 #52A41 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1507.07145

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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