Geodesic
The Proximal Subgradient Formula in Banach Space
Canadian mathematical bulletin, Tome 31 (1988) no. 3, pp. 353-361

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DOI

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.
DOI : 10.4153/CMB-1988-051-9
Mots-clés : proximal normals, proximal subgradients, generalized gradients, Clarke's normalcone, 26B05, 46B20 
The Proximal Subgradient Formula in Banach Space. Canadian mathematical bulletin, Tome 31 (1988) no. 3, pp. 353-361. doi: 10.4153/CMB-1988-051-9
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     title = {The {Proximal} {Subgradient} {Formula} in {Banach} {Space}},
     journal = {Canadian mathematical bulletin},
     pages = {353--361},
     year = {1988},
     volume = {31},
     number = {3},
     doi = {10.4153/CMB-1988-051-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-051-9/}
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