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