New Tour on the Subdifferential of Supremum via Finite Sums and Suprema
本文给出了任意一族凸函数逐点上确界的次微分的新刻画，公式中不涉及上确界有效域的法锥，并揭示了与有限子族上确界次微分的关系，在自反巴拿赫空间中可简化为可数族的上确界。
Abstract This paper provides new characterizations for the subdifferential of the pointwise supremum of an arbitrary family of convex functions. The main feature of our approach is that the normal cone to the effective domain of the supremum (or to finite-dimensional sections of it) does not appear in our formulas. Another aspect of our analysis is that it emphasizes the relationship with the subdifferential of the supremum of finite subfamilies, or equivalently, finite weighted sums. Some specific results are given in the setting of reflexive Banach spaces, showing that the subdifferential of the supremum can be reduced to the supremum of a countable family.