2020/12/09 by Rafael Corrêa, Correa, R., Abderrahim Hantoute +3
Computer Science · Mathematics · #46N10 #52A41 #90C25 #Advanced Optimization Algorithms Research #FOS: Mathematics #Mathematical Inequalities and Applications #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2012.04942
openalex publication_date 2020/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The first part of the paper provides new characterizations of the normal cone to the effective domain of the supremum of an arbitrary family of convex functions. These results are applied in the second part to give new formulas for the subdifferential of the supremum function, which use both the active and nonactive functions at the reference point. Only the data functions are involved in these characterizations, the active ones from one side, together with the nonactive functions multiplied by some appropriate parameters. In contrast with previous works in the literature, the main feature of our subdifferential characterization is that the normal cone to the effective domain of the supremum (or to finite-dimensional sections of this domain) does not appear. A new type of optimality conditions for convex optimization is established at the end of the paper.