Towards Supremum-Sum Subdifferential Calculus Free of Qualification Conditions
研究了两个凸函数和的次微分公式，其中一个函数是任意一族凸函数的上确界，在弱假设下给出了公式，无需连续性条件，统一并扩展了近期文献中的结果。
We give a formula for the subdifferential of the sum of two convex functions where one of them is the supremum of an arbitrary family of convex functions. This is carried out under a weak assumption expressing a natural relationship between the lower semicontinuous envelopes of the data functions in the domain of the sum function. We also provide a new rule for the subdifferential of the sum of two convex functions, which uses a strategy of augmenting the involved functions. The main feature of our analysis is that no continuity-type condition is required. Our approach allows us to unify, recover, and extend different results in the recent literature.