English

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.

Keywords

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}
}