2017/07/12 by Rafael Corrêa, Correa, R., Abderrahim Hantoute +3
Computer Science · Mathematics · #26B05 #26J25 #49H05 #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1707.03782
openalex publication_date 2017/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize and improve the original characterization given by Valadier [18, Theorem 1] of the subdifferential of the pointwise supremum of convex functions, involving the subdifferentials of the data functions at nearby points. We remove the continuity assumption made in that work and obtain a general formula for such a subdiferential. In particular, when the supremum is continuous at some point of its domain, but not necessarily at the reference point, we get a simpler version which gives rise to the Valadier formula. Our starting result is the characterization given in [11, Theorem 4], which uses the epsilon-subdifferential at the reference point.