The Proximal Subgradient Formula in Banach Space
- 1 September 1988
- journal article
- Published by Canadian Mathematical Society in Canadian Mathematical Bulletin
- Vol. 31 (3) , 353-361
- https://doi.org/10.4153/cmb-1988-051-9
Abstract
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
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