Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Florence Jules

Dép. de Mathématiques, Université des Antilles et de la Guyane, 97159 Pointe à Pitre, Guadeloupe, France

fjules@univ-ag.fr

Marc Lassonde

Dép. des Mathématiques, Université des Antilles et de la Guyane, 97159 Pointe à Pitre, Guadeloupe, France

lassonde@univ-ag.fr

Keywords

  • Subdifferential
  • convex function
  • fuzzy sum rule
  • qualification condition
  • nonsmooth analysis

Mathematics Subject Classification

52A41, 26E15; 49J52

Suggested citation

F. Jules, M. Lassonde. “Formulas for Subdifferentials of Sums of Convex Functions.” Journal of Convex Analysis 9 (2002), No. 2, 519–533. https://doi.org/10.68381/jca09030

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Published by Heldermann Verlag, 2002. Rights now held by Banach Press.