Journal of Convex Analysis 32 (2025), No. 1, 227--262
Copyright Heldermann Verlag 2025
A Unified View of Polarity for Functions
Jean-Philippe Chancelier
CERMICS, Ecole Nationale des Ponts et Chaussées, IP Paris, France
jean-philippe.chancelier@enpc.fr
Michel De Lara
CERMICS, Ecole Nationale des Ponts et Chaussées, IP Paris, France
michel.delara@enpc.fr
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.
Keywords: Polarity, bipolar, convex analysis.
MSC: 06D50, 46A20, 46E05, 46N10, 46N15, 52A41.
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