96. Homogeneous convex polyhedra with one unstable equilibrium have at least 7 vertices
Invited abstract in session TB-3: Topics in nonlinear programming, stream contributed papers.
Thursday, 10:00 - 11:30Room: C 104
Authors (first author is the speaker)
| 1. | Sándor Bozóki
|
| SZTAKI | |
| 2. | David Papp
|
| Mathematics, North Carolina State University | |
| 3. | Krisztina Regős
|
| Budapest University of Technology and Economics | |
| 4. | Gábor Domokos
|
| Budapest University of Technology and Economics |
Abstract
The minimal number of vertices of a mono-unstable convex homogenous polyhedron is a challenging open problem. There exists a mono-unstable polyhedra with 18 vertices but it is conjectured non-minimal.
Tetrahedra are never mono-unstable. We improve the lower bound from 5 to 7, i.e., the number of vertices of any mono-unstable, convex homogenous polyhedron is at least 7.
Necessary conditions, in the form of multivariate polynomial inequalities,
for the existence of mono-unstable convex homogenous polyhedron, are developed. The infeasibility of such systems is proved by semidefinite optimization. The result can be verified independently with the supplemented certificates.
Keywords
- Conic and semidefinite optimization
- SS - Semidefinite Optimization
- Large- and Huge-scale optimization
Status: accepted
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