The limiting subdifferential is a generalized concept in variational analysis that extends the idea of subdifferentiation to non-differentiable functions, particularly in cases where the function may not be locally Lipschitz. It represents the set of all possible limiting slopes of a convex function at a given point, capturing the behavior of the function near that point even when traditional derivatives do not exist. This concept is essential for understanding optimality conditions and sensitivity analysis in various applications, especially when dealing with infinite-dimensional spaces.
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