Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Speaker: Michel Thera Title: On the Moreau-Rockafellar-Robinson 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 extendedreal-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. During this presentation, which will summarize a recent joint work with Emil Ernst, we intend to show that this condition is, in a certain sense, also necessary, provided the underlying space is a Banach space. The main result is based upon the existence of a non-supporting weak$^\star$ closed hyperplane to any weak$^\star$- closed and convex unbounded linearly bounded subset of the topological dual of a Banach space.