Abstract

We study the first order variational behavior of the supremum of an arbitrary family of lower semicontinuous functions over a weakly compactly generated β-smooth Banach space. In this context, we present new upper-estimations for the viscosity subdifferential and the Ioffe geometric subdifferential.

Author information

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

Pedro Pérez-Aros

Instituto de Ciencias de la Ingeniería, Universidad de O'Higgins, Rancagua, Chile

pedro.perez@uoh.cl

David Salas

Instituto de Ciencias de la Ingeniería, Universidad de O'Higgins, Rancagua, Chile
and: Centro de Modelamiento Matemático, Universidad de Chile, Santiago, Chile

david.salas@uoh.cl

Emilio Vilches

Instituto de Ciencias de la Ingeniería, Universidad de O'Higgins, Rancagua, Chile

emilio.vilches@uoh.cl

Keywords

  • Supremum function
  • Ioffe geometric subdifferential
  • beta-smooth property
  • first order analysis
  • fuzzy calculus

Mathematics Subject Classification

49J52, 49J53, 49Q10

Suggested citation

P. Pérez-Aros, D. Salas, E. Vilches. “On Formulae for the Ioffe Geometric Subdifferential of a Supremum Function.” Journal of Convex Analysis 27 (2020), No. 2, 487–508. https://doi.org/10.68381/jca27026

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Published by Heldermann Verlag, 2020. Rights now held by Banach Press.