A Unified View of Polarity for Functions

Jean Philippe Chancelier; Michel De Lara

A Unified View of Polarity for Functions

Research output: Contribution to journal › Article › peer-review

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 anti-isomorphic complete 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.

Original language	English
Pages (from-to)	227-262
Number of pages	36
Journal	Journal of Convex Analysis
Volume	35
Issue number	1
Publication status	Published - 1 Jan 2025

Keywords

Polarity
bipolar
convex analysis

Cite this

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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 anti-isomorphic complete 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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AU - De Lara, Michel

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AB - 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 anti-isomorphic complete 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.

KW - Polarity

KW - bipolar

KW - convex analysis

UR - https://www.scopus.com/pages/publications/105006507402

M3 - Article

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SN - 0944-6532

VL - 35

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EP - 262

JO - Journal of Convex Analysis

JF - Journal of Convex Analysis

IS - 1

ER -

A Unified View of Polarity for Functions

Abstract

Keywords

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