“Mono-unstable vertex-heavy convex polyhedra have at least 11 vertices” – CCOR Optimization SeminarSándor Bozóki (Institue for Computer Science and Control (SZTAKI); Corvinus University of Budapest) will hold a presentation entitled “Mono-unstable vertex-heavy convex polyhedra have at least 11 vertices” at the CCOR Optimization Seminar.
The abstract of the seminar:
A polyhedron is called mono-(un)stable if it has exactly one (un)stable static equilibrium point. Here we focus on convex, homogeneous point sets with unit masses at each point (also called vertex-heavy convex polyhedra or polyhedral 0-skeletons). The minimal number of vertices of mono-unstable vertex-heavy convex polyhedra is found. First, the geometric problem is transformed to the (un)solvability of systems of multi-variate polynomial inequalities. Second, up to 10 vertices, infeasibility certificates are generated from the optimal solutions of semidefinite problems. All computations are exact, due to rational arithmetic. This proves that any mono-unstable vertex-heavy convex polyhedron must have at least 11 vertices. This bound is attained: there exist mono-unstable vertex-heavy polyhedra with 11 vertices and 8 faces.
Coauthors: Gábor Domokos, Dávid Papp, Krisztina Regős
We encourage all interested colleagues to participate at this interesting event.