On properties of different notions of centers for convex cones
- Henrion, René
- Seeger, Alberto
2010 Mathematics Subject Classification
- 46B10 46B20 52A41
- Convex cone, central axis, solidity coefficient, sharpness coefficient, revolution cone, ball-generated cone, geometry of Banach spaces
The points on the revolution axis of a circular cone are somewhat special: they are the "most interior'' elements of the cone. This paper addresses the issue of formalizing the concept of center for a convex cone that is not circular. Four distinct proposals are studied in detail: the incenter, the circumcenter, the inner center, and the outer center. The discussion takes place in the context of a reflexive Banach space.
- Set-Valued Var. Anal., 18 (2010) pp. 205--231.