A Unified View of Polarity for Functions
Optimization and Control
2024-10-23 v1
Abstract
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.
Cite
@article{arxiv.2410.16773,
title = {A Unified View of Polarity for Functions},
author = {Jean-Philippe Chancelier and Michel de Lara},
journal= {arXiv preprint arXiv:2410.16773},
year = {2024}
}