Subdifferential Calculus Rules in Convex Analysis: A Unifying Approach Via Pointwise Supremum Functions

We provide a rule to calculate the subdifferential of the pointwise supremum of 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 assumption either on the index set on which the supremum is taken or on the involved functions. Some other calculus rules, namely chain rule formulas of standard type, are obtained from our main result via new and direct proofs. Key words. Convex analysis, convex subdifferential, pointwise supremum function, calculus rules. Mathematics Subject Classification (2000): 52A41, 90C25, 15A39.

• Type: Journal
• Year: 2008
• Where: SIAMJO
• Authors: Abderrahim Hantoute, Marco A. López, Constantin Zalinescu
• Keywords: Locally Convex Topological Vector Space, Pointwise Supremum, SIAMJO 2008, Supremum