A function in a class $\mathcal{F}(X)$ is said to be subdifferentially determined in $\mathcal{F}(X)$ if it is equal up to an additive constant to any function in $\mathcal{F}(X)$ with the same subdifferential. A function is said to be subdifferentially representable if it can be recovered from a subdifferential. We identify large classes of lower semicontinuous functions that possess these properties.
On minimax theorems for lower semicontinuous functions in Hilbert spaces
Subdifferential of the supremum function: Moving back and forth between continuous and non-continuous settings
Subdifferentials of Nonconvex Integral Functionals in Banach Spaces with Applications to Stochastic Dynamic Programming
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