Journal of Convex Analysis 27 (2020), No. 2, 487--508
Copyright Heldermann Verlag 2020
On Formulae for the Ioffe Geometric Subdifferential of a Supremum Function
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
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.
Keywords: Supremum function, Ioffe geometric subdifferential, beta-smooth property, first order analysis, fuzzy calculus.
MSC: 49J52, 49J53, 49Q10.
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