On the Moreau-Rockafellar-Robinson Qualification Condition in Banach Spaces
نویسندگان
چکیده
As well known, the Moreau-Rockafellar-Robinson internal point qualification condition is sufficient to ensure that the infimal convolution of the conjugates of two extended-real-valued convex lower semi-continuous functions defined on a locally convex space is exact, and that the sub-differential of the sum of these functions is the sum of their sub-differentials. This note is devoted to proving that this condition is, in a certain sense, also necessary, provided the underlying space is a Banach space. Our result is based upon the existence of a non-supporting weak -closed hyperplane to any weakclosed and convex unbounded linearly bounded subset of the topological dual of a Banach space.
منابع مشابه
On the necessity of the Moreau-Rockafellar-Robinson qualification condition in Banach spaces
As well known, the Moreau-Rockafellar-Robinson internal point qualification condition is sufficient to ensure that the infimal convolution of the conjugates of two extended-real-valued convex lower semi-continuous functions defined on a locally convex space is exact, and that the subdifferential of the sum of these functions is the sum of their subdifferentials. This note is devoted to proving ...
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