Abstract
This paper studies the class of increasing and co-radiant (ICR) functions over a cone equipped with an order relation which agrees with the conic structure. In particular, a representation of ICR functions as abstract convex functions is provided. This representation suggests the introduction of some polarity notions between sets. The relationship between ICR functions and increasing positively homogeneous functions is also shown.
| Original language | English |
|---|---|
| Pages (from-to) | 561-579 |
| Journal | Journal of Convex Analysis |
| Volume | 15 |
| Issue number | 3 |
| Publication status | Published - 7 Aug 2008 |
Keywords
- Abstract convexity
- Co-normal sets
- Co-radiant sets
- ICR functions
- Monotonic analysis
- Normal sets
- Radiant sets