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An extension of Attouch’s theorem and its application to second-order epi-differentiation of convexly composite functions

An extension of Attouch’s theorem and its application to second-order epi-differentiation of convexly composite functions

In 1977, Hedy Attouch established that a sequence of (closed proper) convex functions epi-converges to a convex function if and only if the graphs of the subdifferentials converge (in the Mosco sense) to the subdifferential of the limiting function and (roughly speaking) there is a condition that fixes the constant …