Year: 2023
Type: article
Abstract: Amenability is a notion of facial exposedness for convex cones that is stronger than being facially dual complete (or ‘nice’) which is, in turn, stronger than merely being facially exposed. Hyperbolicity cones are a family of algebraically structured closed convex cones that contain all spectrahedral cones (linear sections of positive semidefinite cones) as special cases. It is known that all spectrahedral cones are amenable. We establish that all hyperbolicity cones are amenable. As part of the argument, we show that any face of a hyperbolicity cone is a hyperbolicity cone. As a corollary, we show that the intersection of two hyperbolicity cones, not necessarily sharing a common relative interior point, is a hyperbolicity cone.
Source: Mathematical Programming
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,890
Awards: An optimisation-based framework for non-classical Chebyshev approximation, Challenge to Intractable Semidefinite and Second-order Cone Programs, Solving ill-posed conic optimization problems, Realising the potential of hyperbolic programming, Geometry in projection methods and fixed-point theory, Geometry and Conditioning in Structured Conic Problems, G7706312173, Development of Optimization Mathematical Modeling
OpenAlex ID: W3132822607