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The Proximal Subgradient Formula in Banach Space

Published online by Cambridge University Press:  20 November 2018

Philip D. Loewen
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Abstract

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The proximal subgradient formula is a refinement due to Rockafellar of Clarke's fundamental proximal normal formula. It expresses Clarke's generalized gradient of a lower semicontinuous function in terms of analytically simpler proximal subgradients. We use the infinite-dimensional proximal normal formula recently given by Borwein and Strojwas to derive a new version of the proximal subgradient formula in a reflexive Banach space X with Frechet differentiable and locally uniformly convex norm. Our result improves on the one given by Borwein and Strojwas by referring only to the given norm on X.

Keywords

proximal normalsproximal subgradientsgeneralized gradientsClarke's normal cone26B0546B20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 3 , 01 September 1988 , pp. 353 - 361
Copyright
Copyright © Canadian Mathematical Society 1988

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