Journal of Convex Analysis 09 (2002), No. 2, 519--533
Copyright Heldermann Verlag 2002
Formulas for Subdifferentials of Sums of Convex Functions
Florence Jules
Dép. de Mathématiques, Université des Antilles et de la Guyane, 97159 Pointe à Pitre, Guadaloupe, France
fjules@univ-ag.fr
Marc Lassonde
Dép. des Mathématiques, Université des Antilles et de la Guyane, 97159 Pointe à Pitre, Guadaloupe, France
lassonde@univ-ag.fr
We discuss various formulas for the subdifferential of the sum of lower semicontinuous convex functions given in terms of certain topological closure operations on the sum of the subdifferentials of each function. We show how the accuracy of the formulas expressed by the closure operations can be improved when additional assumptions on the family of functions are available.
Keywords: Subdifferential, convex function, fuzzy sum rule, qualification condition, nonsmooth analysis.
MSC: 52A41, 26E15; 49J52
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