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arXiv · 2410.16773

A Unified View of Polarity for Functions

Jean-Philippe Chancelier·Michel de Lara
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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.

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Jean-Philippe Chancelier, Michel de Lara. 2024-10-22. A Unified View of Polarity for Functions. https://arxiv.org/abs/2410.16773

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