SUBDIFFERENTIAL CALCULUS RULES IN CONVEX ANALYSIS: AUNIFYING APPROACH VIA POINTWISE SUPREMUMFUNCTIONS

摘要

We provide a rule to calculate the subdifferential set of the pointwise supremumof an arbitrary family of convex functions defined on a real locally convex topological vector space.Our formula is given exclusively in terms of the data functions and does not require any assumptioneither on the index set on which the supremum is taken or on the involved functions. Some othercalculus rules, namely chain rule formulas of standard type, are obtained from our main result vianew and direct proofs.