Abstract

We explicitly characterize the subdifferential set of the pointwise supremum of an arbitrarily indexed family of lower semi-continuous convex proper functions, deOfined on a locally convex space. Comparing with [11], where equivalent formulas were established using the epsilon-subdifferential for general families of convex functions, the main feature of the current paper is that the resulting characterizations are written exclusively in terms of the Fenchel subdifferential sets of the data functions at nearby points. Hence, we extend to the current setting a similar result due to Valadier which originally requires the continuity of the supremum function at the nominal point.