Abstract: We present different characterizations of the subdifferential of the supremum function of finitely and infinitely indexed families of convex functions under weak continuity assumptions. The resulting formulas are given in terms of the exact subdifferential of the data functions at the
reference point, and not at nearby points. Based on these characterizations we give new Fritz-John and KKT-type optimality conditions for semi-infinite convex optimization, dropping out the typical continuity/closedness assumptions which are usual in the literature. The presentation is a selection of results established in a recent manuscript, entitled “Moreau-Rockafellar type formulas for the subdifferential of the supremum function”, co-authored by R. Correa, A. Hantoute and M.A. López.
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