2024/10/22 by Jean‐Philippe Chancelier, Chancelier, Jean-Philippe, Michel De Lara +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Banach Space Theory #FOS: Mathematics #Optimization and Control (math.OC) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2410.16773
openalex publication_date 2024/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a unified view of the polarity of functions, that encompasses all specific definitions, generalizes several well-known properties and provides new results. We show that bipolar sets and bipolar functions are isomorphic lattices. Also, we explore three possible notions of polar subdifferential associated with a nonnegative function, and we make the connection with the notion of alignement of vectors.