Subdifferential formulae for the supremum of an arbitrary family of\n functions

2018/01/02 by Pedro Pérez-Aros, Pérez-Aros, Pedro
Computer Science · Mathematics · #49J52 #49J53 #49Q10 #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Equations Stability Results #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1801.00724

openalex publication_date 2018/01/02 · openalex created_date 2022/08/13 · openalex updated_date 2026/07/28

Abstract

This work provides calculus for the Fr 'echet and limiting subdifferential of\nthe pointwise supremum given by an arbitrary family of lower semicontinuous\nfunctions. We start our study showing fuzzy results about the Fr 'echet\nsubdifferential of the supremum function. Posteriorly, we study in finite- and\ninfinite-dimensional settings the limiting subdifferential of the supremum\nfunction. Finally, we apply our results to the study of the convex\nsubdifferential; here we recover general formulae for the subdifferential of an\narbitrary family of convex functions.\n

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