A Characterization of Proximal Subgradient Set-Valued Mappings
R. A. Poliquin · Canadian Mathematical Bulletin · 1993
Abstract In this paper we tackle the problem of identifying set-valued mappings that are subgradient set-valued mappings. We show that a set-valued mapping is the proximal subgradient mapping of a lower semicontinuous function bounded below by a quadratic if and only if it satisfies a monotone selection property.