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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Keywords

  • Polarity
  • bipolar
  • convex analysis

Mathematics Subject Classification

06D50, 46A20, 46E05, 46N10, 46N15, 52A41

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Suggested citation

J.-P. Chancelier, M. De Lara. “A Unified View of Polarity for Functions.” Journal of Convex Analysis 32 (2025), No. 1, 227–262. https://doi.org/10.68381/jca32014

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Published by Heldermann Verlag, 2025. Rights now held by Banach Press LLC.