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New formulas for the Fenchel subdifferential of the conjugate function
, 2010
"... Following [13] we provide new formulas for the Fenchel subdifferential of the conjugate of functions defined on locally convex spaces. In particular, this allows deriving expressions for the minimizers set of the lower semicontinuous convex hull of such functions. These formulas are written by means ..."
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Following [13] we provide new formulas for the Fenchel subdifferential of the conjugate of functions defined on locally convex spaces. In particular, this allows deriving expressions for the minimizers set of the lower semicontinuous convex hull of such functions. These formulas are written by means of primal objects related to the subdifferential of the initial function, namely a new enlargement of the Fenchel subdifferential operator.
FréchetLegendre functions and reflexive Banach spaces
"... A 2001 article by Bauschke, Borwein and Combettes [2] showed how to extend naturally the classical definitions of essential smoothness and essential strict convexity from functions on R n in a compatible fashion to any Banach space. They were able, among other things, to show that substantial dual ..."
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A 2001 article by Bauschke, Borwein and Combettes [2] showed how to extend naturally the classical definitions of essential smoothness and essential strict convexity from functions on R n in a compatible fashion to any Banach space. They were able, among other things, to show that substantial duality results hold for Legendre functions in reflexive spaces. That article focused on essential smoothness in the Gâteaux sense. Our goal herein is to show that similar results hold for Fréchet smoothness and to study related properties of such functions on reflexive Banach spaces.