Artículo de revista
Valadier-like Formulas for the Supremum Function II: The compactly indexed case
Fecha
2017Registro en:
Journal of Convex Analysis, Volumen 26, Issue 1, 2017
09446532
Autor
Correa, R.
Hantoute, A.
López, M.
Institución
Resumen
Continuing with the work on the subdifferential of the pointwise supremum of
convex functions, started in Valadier-like formulas for the supremum function I [3],
we focus now on the compactly indexed case. We assume that the index set is
compact and that the data functions are upper semicontinuous with respect to the
index variable (actually, this assumption will only affect the set of ε-active indices
at the reference point). As in the previous work, we do not require any continuity
assumption with respect to the decision variable. The current compact setting gives
rise to more explicit formulas, which only involve subdifferentials at the reference
point of active data functions. Other formulas are derived under weak continuity
assumptions. These formulas reduce to the characterization given by Valadier [18,
Theorem 2] when the supremum function is continuous.