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A characterization of closed convex sets possessing a barrier cone with a nonempty interior is achieved. As a consequence, we describe all the proper extended-valued functionals for which the domain of their Fenchel conjugate has a nonempty interior. We end up the paper by giving an application to the study of the stability of the solution set of a… (More)

When the subdifferential sum rule formula holds for the indicator functions ι C and ι D of two closed convex sets C and D of a locally convex space X, the pair (C, D) is said to have the strong conical hull intersection property (the strong CHIP). The specification of a well-known theorem due to Moreau to the case of the support functionals σ C and σ D… (More)

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… (More)

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