Homogeneous formulas for the subdifferential of the supremum function

R. Correa Fontecilla, R. Correa, A. Hantoute

We provide alternative characterizations of the normal cone to the effective domain of the supremum of an arbitrary family of convex functions. These results are then applied to give new formulas for the subdifferential of the supremum function, which use both the active and nonactive functions at the reference point. In contrast with previous works, the main feature of our subdifferential characterization is that the normal cone to the effective domain of the supremum (or to finite-dimensional sections of this domain) does not appear. The talk also includes a new type of optimality conditions for convex optimization. The results presented in this talk can be found in a joint paper with R. Correa and A. Hantoute.

Keywords: convex analysis, subdifferential, supremum of convex functions

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