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A Characterization of Proximal Subgradient Set-Valued Mappings

Published online by Cambridge University Press:  20 November 2018

R. A. Poliquin
R. A. Poliquin*
Affiliation:
Department of Mathematics University of Alberta Edmonton, Alberta T6G 2G1
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Abstract

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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.

Keywords

49A5258C0658C2065K10proximal subgradientsnonsmooth analysisquadratic conjugateset-valued mappingsmonotone mappinggeneralized subgradientsstrictly submonotonecyclically submonotone
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 1 , 01 March 1993 , pp. 116 - 122
Copyright
Copyright © Canadian Mathematical Society 1993

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